7 1 statistics homework

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AP®︎/College Statistics

Unit 1: exploring categorical data, unit 2: exploring one-variable quantitative data: displaying and describing, unit 3: exploring one-variable quantitative data: summary statistics, unit 4: exploring one-variable quantitative data: percentiles, z-scores, and the normal distribution, unit 5: exploring two-variable quantitative data, unit 6: collecting data, unit 7: probability, unit 8: random variables and probability distributions, unit 9: sampling distributions, unit 10: inference for categorical data: proportions, unit 11: inference for quantitative data: means, unit 12: inference for categorical data: chi-square, unit 13: inference for quantitative data: slopes, unit 14: prepare for the 2022 ap®︎ statistics exam.

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Chapter 1: Sampling and Data

Chapter 1 Homework

Homework from 1.2.

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

The population is all of the clients of the fitness center. A sample of the clients that use the fitness center for a given week. The average amount of time that all clients exercise in one week. The average amount of time that a sample of clients exercises in one week. The amount of time that a client exercises in one week. Examples are: 2 hours, 5 hours, and 7.5 hours –>

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

• all children who take ski or snowboard lessons
• a group of these children
• the population mean age of children who take their first snowboard lesson
• the sample mean age of children who take their first snowboard lesson
• X = the age of one child who takes his or her first ski or snowboard lesson
• values for X , such as 3, 7, and so on

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

the cardiologist’s patients a group of the cardiologist’s patients the mean recovery period of all of the cardiologist’s patients the mean recovery period of the group of the cardiologist’s patients X = the mean recovery period of one patient values for X, such as 10 days, 14 days, 20 days, and so on –>

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

• the clients of the insurance companies
• a group of the clients
• the mean health costs of the clients
• the mean health costs of the sample
• X = the health costs of one client
• values for X , such as 34, 9, 82, and so on

A politician is interested in the proportion of voters in his district who think he is doing a good job.

all voters in the politician’s district a random selection of voters in the politician’s district the proportion of voters in this district who think this politician is doing a good job the proportion of voters in this district who think this politician is doing a good job in the sample X = the number of voters in the district who think this politician is doing a good job Yes, he is doing a good job. No, he is not doing a good job. –>

A marriage counselor is interested in the proportion of clients she counsels who stay married.

• all the clients of this counselor
• a group of clients of this marriage counselor
• the proportion of all her clients who stay married
• the proportion of the sample of the counselor’s clients who stay married
• X = the number of couples who stay married

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

all voters (in a certain geographic area) a random selection of all the voters the proportion of voters who are interested in this particular cause the proportion of voters who are interested in this particular cause in the sample X = the number of voters who are interested in this particular cause yes, no –>

A marketing company is interested in the proportion of people who will buy a particular product.

• all people (maybe in a certain geographic area, such as the United States)
• a group of the people
• the proportion of all people who will buy the product
• the proportion of the sample who will buy the product
• X = the number of people who will buy it
• buy, not buy

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following:

[latex]X[/latex] = number of days a Lake Tahoe Community College math student is absent

In this case, X is an example of a:

• population.

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of a:

More Homework from 1.2

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

quantitative discrete, 150

percentage of body fat

quantitative continuous, 19.2% –>

favorite baseball team

qualitative, Oakland A’s

time in line to buy groceries

quantitative continuous, 7.2 minutes –>

number of students enrolled at Evergreen Valley College

quantitative discrete, 11,234 students

most-watched television show

qualitative, Dancing with the Stars –>

brand of toothpaste

qualitative, Crest

distance to the closest movie theater

quantitative continuous, 8.32 miles –>

age of executives in Fortune 500 companies

quantitative continuous, 47.3 years

number of competing computer spreadsheet software packages

quantitative discrete, three –>

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

“Number of times per week” is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

“Duration (amount of time)” is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

The survey would not be a true representation of the entire population of air travelers.

Conducting the survey on a holiday weekend will not produce representative results.

• Conduct the survey during different times of the year.

Conduct the survey using flights to and from various locations.

Conduct the survey on different days of the week.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Answers will vary. Sample Answer: Randomly choose 25 colleges in the state. Use all statistics classes from each of the chosen colleges in the sample. This can be done by listing all the colleges together with a two-digit number starting with 00 then 01, etc. The list of colleges can be found on Wikipedia. http://en.wikipedia.org/wiki/List_of_colleges_and_universities_in_California Use a random number generator to pick 25 colleges. –>

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Answers will vary. Sample Answer: You could use a systematic sampling method. Stop the tenth person as they leave one of the buildings on campus at 9:50 in the morning. Then stop the tenth person as they leave a different building on campus at 1:50 in the afternoon.

List some practical difficulties involved in getting accurate results from a telephone survey.

Answers will vary. Sample Answer: Not all people have a listed phone number. Many people hang up or do not respond to phone surveys. –>

List some practical difficulties involved in getting accurate results from a mailed survey.

Answers will vary. Sample Answer: Many people will not respond to mail surveys. If they do respond to the surveys, you can’t be sure who is responding. In addition, mailing lists can be incomplete.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

Ask everyone to include their age then take a random sample from the data. Include in the report how the survey was conducted and why the results may not be accurate. –>

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was:

• simple random

Name the sampling method used in each of the following situations:

convenience cluster stratified systematic simple random

A “random survey” was conducted of 3,274 people of the “microprocessor generation” (people born since 1971, the year the microprocessor was invented). It was reported that 48% of those individuals surveyed stated that if they had 💲2,000 to spend, they would use it for computer equipment. Also, 66% of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?

Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute’s road show called “America’s Smithsonian.”

• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

Yes, in polling, samples that are from 1,200 to 1,500 observations are considered large enough and good enough if the survey is random and is well done. We do not have enough information to decide if this is a random sample from the U.S. population. No, this is a convenience sample taken from individuals who visited an exhibition in the Angeles Convention Center. This sample is not representative of the U.S. population. It is possible that the two sample statistics, 48% and 66% are larger than the true parameters in the population at large. In any event, no conclusion about the population proportions can be inferred from this convenience sample. –>

The Gallup-Healthways Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 Presidential Election, a magazine titled Literary Digest released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent postcards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, George Gallup conducted his own poll of 30,000 prospective voters. His researchers used a method they called “quota sampling” to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

The country was in the middle of the Great Depression, and many people could not afford these “luxury” items and therefore were not able to be included in the survey. Samples that are too small can lead to sampling bias. sampling error stratified

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI’s Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in [link] could explain this connection?

Causality: The fact that two variables are related does not guarantee that one variable is influencing the other. We cannot assume that crime rate impacts education level or that education level impacts crime rate.

Confounding: There are many factors that define a community other than education level and crime rate. Communities with high crime rates and high education levels may have other lurking variables that distinguish them from communities with lower crime rates and lower education levels. Because we cannot isolate these variables of interest, we cannot draw valid conclusions about the connection between education and crime. Possible lurking variables include police expenditures, unemployment levels, region, average age, and size.

YouPolls is a website that allows anyone to create and respond to polls. One question posted April 15 asks:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” 1

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

Self-Selected Samples: Only people who are interested in the topic are choosing to respond. Sample Size Issues: A sample with only 11 participants will not accurately represent the opinions of a nation. Undue Influence: The question is wording in a specific way to generate a specific response. Self-Funded or Self-Interest Studies: This question was generated to support one person’s claim and it was designed to get the answer that the person desires. –>

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.” 2

The Pew Research Center for People and the Press admits:

“The percentage of people we interview – out of all we try to interview – has been declining over the past decade or more.” 3

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.
• Possible reasons: increased use of caller id, decreased use of landlines, increased use of private numbers, voice mail, privacy managers, hectic nature of personal schedules, decreased willingness to be interviewed
• When a large number of people refuse to participate, then the sample may not have the same characteristics of the population. Perhaps the majority of people willing to participate are doing so because they feel strongly about the subject of the survey.

Bringing It Together

Seven hundred and seventy-one distance learning students at Long Beach City College responded to surveys in the 2010-11 academic year. Highlights of the summary report are listed in [link] .

• What percentage of the students surveyed do not have a computer at home?
• About how many students in the survey live at least 16 miles from campus?
• If the same survey were done at Great Basin College in Elko, Nevada, do you think the percentages would be the same? Why?

4% 13% Not necessarily. Long Beach City is the seventh largest college in California, and it has an enrollment of approximately 27,000 students. On the other hand, Great Basin College has its campuses in rural northeastern Nevada, and its enrollment of about 3,500 students. –>

Several online textbook retailers advertise that they have lower prices than on-campus bookstores. However, an important factor is whether the Internet retailers actually have the textbooks that students need in stock. Students need to be able to get textbooks promptly at the beginning of the college term. If the book is not available, then a student would not be able to get the textbook at all, or might get a delayed delivery if the book is back ordered.

A college newspaper reporter is investigating textbook availability at online retailers. He decides to investigate one textbook for each of the following seven subjects: calculus, biology, chemistry, physics, statistics, geology, and general engineering. He consults textbook industry sales data and selects the most popular nationally used textbook in each of these subjects. He visits websites for a random sample of major online textbook sellers and looks up each of these seven textbooks to see if they are available in stock for quick delivery through these retailers. Based on his investigation, he writes an article in which he draws conclusions about the overall availability of all college textbooks through online textbook retailers.

Write an analysis of his study that addresses the following issues: Is his sample representative of the population of all college textbooks? Explain why or why not. Describe some possible sources of bias in this study, and how it might affect the results of the study. Give some suggestions about what could be done to improve the study.

Answers will vary. Sample answer: The sample is not representative of the population of all college textbooks. Two reasons why it is not representative are that he only sampled seven subjects and he only investigated one textbook in each subject. There are several possible sources of bias in the study. The seven subjects that he investigated are all in mathematics and the sciences; there are many subjects in the humanities, social sciences, and other subject areas (for example: literature, art, history, psychology, sociology, business) that he did not investigate at all. It may be that different subject areas exhibit different patterns of textbook availability, but his sample would not detect such results.

He also looked only at the most popular textbook in each of the subjects he investigated. The availability of the most popular textbooks may differ from the availability of other textbooks in one of two ways:

• the most popular textbooks may be more readily available online, because more new copies are printed, and more students nationwide are selling back their used copies, OR
• the most popular textbooks may be harder to find available online, because more student demand exhausts the supply more quickly.

In reality, many college students do not use the most popular textbooks in their subject, and this study gives no useful information about the situation for those less popular textbooks.

He could improve this study by:

• expanding the selection of subjects he investigates so that it is more representative of all subjects studied by college students, and
• expanding the selection of textbooks he investigates within each subject to include a mixed representation of both the most popular and less popular textbooks.

HOMEWORK from 1.3

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below:

• Fill in the blanks in [link] .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in [link] .

• What percent of adults flossed six times per week?
• What percentage flossed at most three times per week?

Nineteen immigrants to the U.S were asked how many years, to the nearest year, they have lived in the U.S. The data are as follows: 2 5 7 2 2 10 20 15 0 7 0 20 5 12 15 12 4 5 10 .

[link] was produced.

• Fix the errors in [link] . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the U.S. for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the U.S. five or seven years?
• What fraction of the people surveyed have lived in the U.S. at most 12 years?
• What fraction of the people surveyed have lived in the U.S. fewer than 12 years?
• What fraction of the people surveyed have lived in the U.S. from five to 20 years, inclusive?

The Frequencies for 15 and 20 should both be two and the Relative Frequencies should both be

The mistake could be due to copying the data down wrong. The Cumulative Relative Frequency for five years should be 0.4737. The mistake is due to calculating the Relative Frequency instead of the Cumulative Relative Frequency. The Cumulative Relative Frequency for 15 years should be 0.8947 The 47% is the Cumulative Relative Frequency, not the Relative Frequency. 47% of the people surveyed have lived in the U.S. for five years or less.

How much time does it take to travel to work? [link] shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

The sum of the travel times is 1,173.1. Divide the sum by 50 to calculate the mean value: 23.462. Because each state’s travel time was measured to the nearest tenth, round this calculation to the nearest hundredth: 23.46.

Forbes magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least 💲5 per share, and have reported annual revenue between 💲5 million and 💲1 billion. [link] shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

26 (This is the count of CEOs in the 55 to 59 and 60 to 64 categories.) 12% (number of CEOs age 65 or older ÷ total number of CEOs) 14/60; 0.23; 23% 0.45 Graph A represents the cumulative relative frequency, and Graph B shows the relative frequency. –>

Use the following information to answer the next two exercises: [link] contains data on hurricanes that have made direct hits on the U.S. Between 1851 and 2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• Not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

HOMEWORK 1.4

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

Explanatory variable: amount of sleep

Response variable: performance measured in assigned tasks

Treatments: normal sleep and 27 hours of total sleep deprivation

Experimental Units: 19 professional drivers

Lurking variables: none – all drivers participated in both treatments

Random assignment: treatments were assigned in random order; this eliminated the effect of any “learning” that may take place during the first experimental session

Control/Placebo: completing the experimental session under normal sleep conditions

Blinding: researchers evaluating subjects’ performance must not know which treatment is being applied at the time

An advertisement for Acme Investments displays the two graphs in [link] to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graphs do not show scales of values. We do not know the period of time each graph represents; they may show data from different years. We also do not know if the vertical scales on each graph are equivalent. The scales may have been adjusted to exaggerate or minimize trends. There is no reliable information to be gleaned from these graphs, and setting them up as examples of performance is misleading. –>

The graph in [link] shows the number of complaints for six different airlines as reported to the US Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

You cannot assume that the numbers of complaints reflect the quality of the airlines. The airlines shown with the greatest number of complaints are the ones with the most passengers. You must consider the appropriateness of methods for presenting data; in this case displaying totals is misleading.

Introductory Statistics Copyright © 2024 by LOUIS: The Louisiana Library Network is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License , except where otherwise noted.

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11 Surprising Homework Statistics, Facts & Data

The age-old question of whether homework is good or bad for students is unanswerable because there are so many “ it depends ” factors.

For example, it depends on the age of the child, the type of homework being assigned, and even the child’s needs.

There are also many conflicting reports on whether homework is good or bad. This is a topic that largely relies on data interpretation for the researcher to come to their conclusions.

To cut through some of the fog, below I’ve outlined some great homework statistics that can help us understand the effects of homework on children.

Homework Statistics List

1. 45% of parents think homework is too easy for their children.

A study by the Center for American Progress found that parents are almost twice as likely to believe their children’s homework is too easy than to disagree with that statement.

Here are the figures for math homework:

• 46% of parents think their child’s math homework is too easy.
• 25% of parents think their child’s math homework is not too easy.
• 29% of parents offered no opinion.

Here are the figures for language arts homework:

• 44% of parents think their child’s language arts homework is too easy.
• 28% of parents think their child’s language arts homework is not too easy.
• 28% of parents offered no opinion.

These findings are based on online surveys of 372 parents of school-aged children conducted in 2018.

2. 93% of Fourth Grade Children Worldwide are Assigned Homework

The prestigious worldwide math assessment Trends in International Maths and Science Study (TIMSS) took a survey of worldwide homework trends in 2007. Their study concluded that 93% of fourth-grade children are regularly assigned homework, while just 7% never or rarely have homework assigned.

3. 17% of Teens Regularly Miss Homework due to Lack of High-Speed Internet Access

A 2018 Pew Research poll of 743 US teens found that 17%, or almost 2 in every 5 students, regularly struggled to complete homework because they didn’t have reliable access to the internet.

This figure rose to 25% of Black American teens and 24% of teens whose families have an income of less than $30,000 per year.

4. Parents Spend 6.7 Hours Per Week on their Children’s Homework

A 2018 study of 27,500 parents around the world found that the average amount of time parents spend on homework with their child is 6.7 hours per week. Furthermore, 25% of parents spend more than 7 hours per week on their child’s homework.

American parents spend slightly below average at 6.2 hours per week, while Indian parents spend 12 hours per week and Japanese parents spend 2.6 hours per week.

5. Students in High-Performing High Schools Spend on Average 3.1 Hours per night Doing Homework

A study by Galloway, Conner & Pope (2013) conducted a sample of 4,317 students from 10 high-performing high schools in upper-middle-class California. 

Across these high-performing schools, students self-reported that they did 3.1 hours per night of homework.

Graduates from those schools also ended up going on to college 93% of the time.

6. One to Two Hours is the Optimal Duration for Homework

A 2012 peer-reviewed study in the High School Journal found that students who conducted between one and two hours achieved higher results in tests than any other group.

However, the authors were quick to highlight that this “t is an oversimplification of a much more complex problem.” I’m inclined to agree. The greater variable is likely the quality of the homework than time spent on it.

Nevertheless, one result was unequivocal: that some homework is better than none at all : “students who complete any amount of homework earn higher test scores than their peers who do not complete homework.”

7. 74% of Teens cite Homework as a Source of Stress

A study by the Better Sleep Council found that homework is a source of stress for 74% of students. Only school grades, at 75%, rated higher in the study.

That figure rises for girls, with 80% of girls citing homework as a source of stress.

Similarly, the study by Galloway, Conner & Pope (2013) found that 56% of students cite homework as a “primary stressor” in their lives.

8. US Teens Spend more than 15 Hours per Week on Homework

The same study by the Better Sleep Council also found that US teens spend over 2 hours per school night on homework, and overall this added up to over 15 hours per week.

Surprisingly, 4% of US teens say they do more than 6 hours of homework per night. That’s almost as much homework as there are hours in the school day.

The only activity that teens self-reported as doing more than homework was engaging in electronics, which included using phones, playing video games, and watching TV.

9. The 10-Minute Rule

The National Education Association (USA) endorses the concept of doing 10 minutes of homework per night per grade.

For example, if you are in 3rd grade, you should do 30 minutes of homework per night. If you are in 4th grade, you should do 40 minutes of homework per night.

However, this ‘rule’ appears not to be based in sound research. Nevertheless, it is true that homework benefits (no matter the quality of the homework) will likely wane after 2 hours (120 minutes) per night, which would be the NEA guidelines’ peak in grade 12.

10. 21.9% of Parents are Too Busy for their Children’s Homework

An online poll of nearly 300 parents found that 21.9% are too busy to review their children’s homework. On top of this, 31.6% of parents do not look at their children’s homework because their children do not want their help. For these parents, their children’s unwillingness to accept their support is a key source of frustration.

11. 46.5% of Parents find Homework too Hard

The same online poll of parents of children from grades 1 to 12 also found that many parents struggle to help their children with homework because parents find it confusing themselves. Unfortunately, the study did not ask the age of the students so more data is required here to get a full picture of the issue.

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Interpreting the Data

Unfortunately, homework is one of those topics that can be interpreted by different people pursuing differing agendas. All studies of homework have a wide range of variables, such as:

• What age were the children in the study?
• What was the homework they were assigned?
• What tools were available to them?
• What were the cultural attitudes to homework and how did they impact the study?
• Is the study replicable?

The more questions we ask about the data, the more we realize that it’s hard to come to firm conclusions about the pros and cons of homework .

Furthermore, questions about the opportunity cost of homework remain. Even if homework is good for children’s test scores, is it worthwhile if the children consequently do less exercise or experience more stress?

Thus, this ends up becoming a largely qualitative exercise. If parents and teachers zoom in on an individual child’s needs, they’ll be able to more effectively understand how much homework a child needs as well as the type of homework they should be assigned.

Related: Funny Homework Excuses

The debate over whether homework should be banned will not be resolved with these homework statistics. But, these facts and figures can help you to pursue a position in a school debate on the topic – and with that, I hope your debate goes well and you develop some great debating skills!

Chris Drew (PhD)

Dr. Chris Drew is the founder of the Helpful Professor. He holds a PhD in education and has published over 20 articles in scholarly journals. He is the former editor of the Journal of Learning Development in Higher Education. [Image Descriptor: Photo of Chris]

• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 5 Top Tips for Succeeding at University
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 50 Durable Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 100 Consumer Goods Examples
• Chris Drew (PhD) https://helpfulprofessor.com/author/chris-drew-phd/ 30 Globalization Pros and Cons

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North Carolina vs. Alabama odds, prediction: 2024 NCAA Tournament picks, Sweet 16 best bets from proven model

Sportsline's model has made its march madness 2024 picks for alabama crimson tide vs. unc tar heels in the sweet 16 on thursday.

The North Carolina Tar Heels will look to even the score with the Alabama Crimson Tide on Thursday when they meet in a 2024 NCAA Tournament Sweet 16 showdown. The No. 1-seeded Tar Heels and No. 4-seeded Crimson Tide cruised through the first two rounds with a pair of blowout victories but that will likely change on Thursday. Last year, the clubs met in the Phil Knight Invitational and the Crimson Tide prevailed 103-101 in four overtimes. The loss impacted the resume of North Carolina, which failed to reach the NCAA Tournament last season. A revenge win would send the Tar Heels to the Elite Eight.

Tipoff is set for 9:39 p.m. ET from Crypto.com Arena in Los Angeles. The Tar Heels are 4.5-point favorites and the over/under for total points scored is 173.5 in the latest North Carolina vs. Alabama odds via SportsLine consensus. Before making any Alabama vs. North Carolina picks, you need to  check out the college basketball analysis from the SportsLine Projection Model . 

The model simulates every Div. I college basketball game 10,000 times. It enters the Sweet 16 round of the 2024 NCAA tournament on a 152-109 roll on all top-rated  college basketball picks  dating back to last season, returning more than $1,800 for $100 players. It also has a strong 32-21 (+890) record on top-rated spread picks this season, and it called 13 Sweet 16 teams this year. Anyone following it has seen huge returns.

Now, the model has set its sights on UNC vs. Alabama and just locked in its March Madness predictions. You can  visit SportsLine now to see the model's picks . Here are several college basketball odds and betting lines  and trends for Alabama vs. UNC:

• North Carolina vs. Alabama spread: UNC -4.5
• North Carolina vs. Alabama over/under: 173.5
• North Carolina vs. Alabama money line: UNC -199, Alabama +165
• BAMA: The Crimson Tide are 3-1 ATS this season when playing on fewer days' rest than their opponent.
• UNC: The Tar Heels are 8-4 ATS this season following four or more days off.
• North Carolina vs. Alabama picks: See picks at SportsLine

Why North Carolina can cover

Although the Tar Heels are one of the top rebounding teams in the nation at nearly 41 boards per game, they sometimes still have to shake the reputation of being a finesse team that would rather win shootouts than exert physical dominance over its opponents. Coach Hubert Davis agreed with this assessment during the first half against Michigan State in which the Spartans, who are historically known for their grit, outworked the Tar Heels while leading for most of the first half.  

Davis said he lit into his team during a timeout and implored the Tar Heels to match Michigan State's intensity. Senior forward Armando Bacot led the way by muscling inside for high-percentage shots and rebounds, and his teammates followed his lead. North Carolina went on a 23-3 run to take control of the game. Bacot finished with 18 points, seven rebounds, three assists and two blocks against the Spartans. For the season, Bacot is averaging 14.4 points and 10.2 rebounds per game.  See which team to back at SportsLine . 

Why Alabama can cover

Alabama got some good news when coach Nate Oats announced earlier this week that sharp-shooting junior Latrell Wrightsell will be available for Thursday's game after he left the contest against Grand Canyon with a head injury. Wrightsell, who is a transfer from Cal State Fullerton , missed four games earlier this season because of a concussion and also missed part of the Crimson Tide's NCAA Tournament opener against Charleston because of an injury. The junior had just two points in 11 minutes in the second round against Grand Canyon.

Wrightsell is averaging 9.3 points per game this season and his 44.3% accuracy from 3-point range is the best for any Alabama player who averages at least 20 minutes per game. He also has scored at least 19 points on five occasions this season.  See which team to back at SportsLine . 

How to make Alabama vs. UNC picks

SportsLine's model is leaning Under on the total, projecting the teams to combine for 162 points. The model also says one side of the spread hits almost 70% of the time.  You can see the picks only at SportsLine . 

So who wins UNC vs. Alabama, and which side of the spread hits nearly 70% of the time? Visit SportsLine now to see which side of the spread you need to jump on, all from the model on a 152-109 roll on its top-rated college basketball picks , and find out.

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An official website of the United States government

Gross Domestic Product by State and Personal Income by State, 4th Quarter 2023 and Preliminary 2023

• News Release
• Related Materials
• Additional Information

Real gross domestic product (GDP) increased in all 50 states and the District of Columbia in the fourth quarter of 2023, with the percent change ranging from 6.7 percent in Nevada to 0.2 percent in Nebraska (table 1), according to statistics released today by the U.S. Bureau of Economic Analysis (BEA). Current-dollar GDP increased in 49 states and the District of Columbia. For the year 2023 , real, or inflation-adjusted, GDP also increased in 49 states and the District of Columbia.

Personal income , in current dollars, increased in all 50 states and the District of Columbia in the fourth quarter of 2023, with the percent change ranging from 6.7 percent in Nevada to 0.8 percent in Iowa and North Dakota (table 4). For the year 2023 , current-dollar personal income also increased in all 50 states and the District of Columbia.

Quarterly GDP

In the fourth quarter of 2023, real GDP for the nation grew at an annual rate of 3.4 percent. Real GDP increased in 18 of the 23 industry groups for which BEA prepares quarterly state estimates (table 2). Nondurable-goods manufacturing, retail trade, and durable-goods manufacturing were the leading contributors to growth in real GDP nationally.

• Construction, which increased in 45 states and the District of Columbia, was the leading contributor to growth in 3 states including Nevada, the state with the largest increase in real GDP.
• Agriculture, forestry, fishing, and hunting, which increased nationally and in 32 states, was the leading contributor to growth in Idaho, the state with the second-largest increase in real GDP. In contrast, this industry was the leading offset to growth in Nebraska and Kansas, the states with the smallest increases in real GDP.
• Retail trade, which increased in all 50 states and the District of Columbia, was the leading contributor to growth in 14 states including Utah, the state with the third-largest increase in real GDP.

In 2023, real GDP for the nation grew at an annual rate of 2.5 percent, with the percent change ranging from 5.9 percent in North Dakota to –1.2 percent in Delaware. Real GDP increased in 17 of the 23 industry groups for which BEA prepares preliminary annual state estimates (table 3). Retail trade; professional, scientific, and technical services; and health care and social assistance were the leading contributors to growth in real GDP nationally.

• Mining increased in 43 states. This industry was the leading contributor to growth in seven states including North Dakota, Texas, Wyoming, Alaska, and Oklahoma, the states with the first-, second-, third-, fourth-, and fifth-largest increases in real GDP, respectively.
• Retail trade increased in all 50 states and the District of Columbia. This industry was the leading contributor to growth in 23 states including Florida, the state with the seventh-largest increase in real GDP.
• Health care and social assistance increased in 49 states and the District of Columbia. This industry was the leading contributor to growth in 6 states.
• Finance and insurance decreased in 43 states and the District of Columbia. The industry was the leading contributor to the decline in Delaware.

Quarterly personal income

In the fourth quarter of 2023, current-dollar personal income increased $229.4 billion, or 4.0 percent at an annual rate (table 4). Increases in earnings and property income (dividends, interest, and rent) were partially offset by a decrease in transfer receipts (chart 1).

Earnings increased in 48 states and the District of Columbia, while growing 4.6 percent nationally (table 5). The percent change in earnings ranged from 8.5 percent in Nevada to –0.8 percent in North Dakota.

• Earnings increased in 20 of the 24 industries for which BEA prepares quarterly estimates (table 6).
• Construction earnings increased in 48 states and the District of Columbia. This industry was the leading contributor to growth in personal income in Nevada and Idaho, the states with the largest and third-largest increases in personal income, respectively.
• In South Carolina, the state with the second-largest increase in personal income, growth in earnings in the construction and professional, scientific, and technical services industries were the leading contributors to the increase in personal income.
• Decreases in farm earnings were the leading offsets to growth in Iowa and North Dakota, the states with the smallest increases in personal income.

Property income increased in all 50 states and the District of Columbia, while growing 6.7 percent nationally. The percent change ranged from 8.8 percent in Florida to 4.7 percent in Iowa and Mississippi (table 5).

Transfer receipts decreased in 32 states and the District of Columbia, while declining 0.7 percent nationally. The percent change in transfer receipts ranged from 8.1 percent in Mississippi to –5.0 percent in Arizona (table 5).

Annual personal income

In 2023, personal income for the nation increased at an annual rate of 5.2 percent, with the percent change ranging from 7.0 percent in Florida to 3.4 percent in Indiana.

Nationally, increases in earnings, property income, and transfer receipts contributed to the increase in personal income (chart 2).

Earnings increased in all 50 states and the District of Columbia, while growing 5.6 percent nationally. The percent change in earnings ranged from 8.5 percent in Alaska to 4.0 percent in Mississippi (table 7).

• Earnings increased in 21 of the 24 industries for which BEA prepares annual estimates (table 8).
• In Florida, the state with the largest increase in personal income, growth in earnings in the professional, scientific, and technical services and in the health care and social assistance industries were the leading contributors to the increase in personal income.
• In Utah and Wyoming, the states with the second- and third-largest increases in personal income, growth in earnings in state and local government was the leading contributor to the increase in personal income.

Property income increased in all 50 states and the District of Columbia, while growing 6.3 percent nationally. The percent change ranged from 9.0 percent in Idaho to 2.7 percent in Iowa (table 7).

Transfer receipts increased in 45 states and the District of Columbia, while growing 2.5 percent nationally. The percent change in transfer receipts ranged from 7.3 percent in the District of Columbia to –8.9 percent in Alaska (table 7).

Update of state statistics

Today, BEA also released revised quarterly estimates of personal income by state for the first quarter of 2023 through the third quarter of 2023. This update incorporates new and revised source data that are more complete and more detailed than previously available and aligns the states with the national estimates from the National Income and Product Accounts released on March 28, 2024.

BEA also released new estimates of per capita personal income for the fourth quarter of 2023, along with revised estimates for the first quarter of 2020 through the third quarter of 2023. BEA used U.S. Census Bureau (Census) population figures to calculate per capita personal income estimates for the first quarter of 2020 through the fourth quarter of 2023. BEA also used new Census population figures to update annual 2020 to 2022 per capita personal income statistics and to produce new per capita personal income statistics for 2023. For earlier estimates, BEA continues to use intercensal population statistics that it developed based on Census methodology. See “ Note on Per Capita Personal Income and Population .”

*          *          *

Next release: June 28, 2024, at 10:00 a.m. EDT Gross Domestic Product by State and Personal Income by State, 1st Quarter 2024

Full Release & Tables (PDF)

Tables only (excel), quarterly highlights (pdf), annual highlights (pdf), interactive tables.

• Technical (GDP) Clifford Woodruff 301-278-9234 [email protected]
• Technical (Income) Matthew von Kerczek 301-278-9250 [email protected]
• Media (BEA) Connie O'Connell 301-278-9003 [email protected]
• Stay informed about BEA developments by reading The BEA Wire , signing up for BEA's email subscription service , or following @BEA_News on X, formerly known as Twitter.
• Historical time series for these estimates can be accessed in BEA's Interactive Data Application .
• Access BEA data by registering for BEA's Data Application Programming Interface .
• For more on BEA's statistics, see our online journal, the Survey of Current Business .
• For upcoming economic indicators, see BEA's news release schedule .
• BEA Regional Facts ( BEARFACTS ) is a narrative summary of personal income, per capita personal income, components of income, and gross domestic product for counties, metropolitan statistical areas, and states.
• For complete information on the sources and methods used to estimate gross domestic product and personal income by state, see BEA's gross domestic product by state and state personal income and employment methodologies.

Definitions

Gross domestic product (GDP) by state is the market value of goods and services produced by the labor and property located in a state. GDP by state is the state counterpart of the nation's GDP, the Bureau's featured and most comprehensive measure of U.S. economic activity.

Current-dollar statistics are valued in the prices of the period when the transactions occurred—that is, at “market value.” They are also referred to as “nominal GDP” or “current-price GDP.”

Real values are inflation-adjusted statistics—that is, these exclude the effects of price changes.

Contributions to growth are an industry’s contribution to the state’s overall percent change in real GDP. The contributions are additive and can be summed to the state’s overall percent change.

Personal income is the income received by, or on behalf of, all persons from all sources: from participation as laborers in production, from owning a home or business, from the ownership of financial assets, and from government and business in the form of transfers. It includes income from domestic sources as well as the rest of world. It does not include realized or unrealized capital gains or losses.

Personal income is measured before the deduction of personal income taxes and other personal taxes and is reported in current dollars (no adjustment is made for price changes).

State personal income differs slightly from the estimate of U.S. personal income in the National Income and Product Accounts because of differences in coverage, in the methodologies used to prepare the estimates, and in the timing of the availability of source data. In BEA’s state statistics, estimates of personal income for the United States is the sum of the state estimates and the estimate for the District of Columbia.

Per capita personal income is calculated as the total personal income of the residents of a state divided by the population of the state. In computing per capita personal income, BEA uses mid-quarter population estimates based on unpublished U.S. Census Bureau data.

Earnings by place of work is the sum of wages and salaries, supplements to wages and salaries, and proprietors’ income. BEA’s industry estimates are presented on an earnings by place-of-work basis.

Net earnings by place of residence is earnings by place of work less contributions for government social insurance plus an adjustment to convert earnings by place of work to a place-of-residence basis. BEA presents net earnings on an all-industry level.

Property income is rental income of persons, personal dividend income, and personal interest income.

Personal current transfer receipts are benefits received by persons from federal, state, and local governments and from businesses for which no current services are performed. They include retirement and disability insurance benefits (mainly social security), medical benefits (mainly Medicare and Medicaid), income maintenance benefits, unemployment insurance compensation, veterans’ benefits, and federal education and training assistance.

Statistical conventions

Quarter-to-quarter percent changes are calculated from unrounded data and are annualized. Annualized growth rates show the rate of change that would have occurred had the pattern been repeated over four quarters (1 year). Annualized rates of change can be calculated as follows: (((level of later quarter / level of earlier quarter)^4)-1)*100. Quarterly estimates are expressed at seasonally adjusted annual rates unless otherwise specified. Quarter-to-quarter dollar changes are differences between published estimates.

Seasonal adjustment and annual rates . Quarterly values are expressed at seasonally adjusted annual rates. For details, see the FAQ " Why does BEA publish estimates at annual rates? " on the BEA website.

Quantities and prices . Quantities, or “real” measures, are expressed as index numbers with a specified reference year equal to 100 (currently 2017). Quantity indexes are calculated using a Fisher chain-weighted formula that incorporates weights from two adjacent periods (quarters for quarterly data and annuals for annual data). “Real” dollar series are calculated by multiplying the quantity index by the current dollar value in the reference year and then dividing by 100. Percent changes calculated from chained-dollar levels and quantity indexes are conceptually the same; any differences are due to rounding.

Chained-dollar values are not additive, because the relative weights for a given period differ from those of the reference year.

Chained-dollar values of GDP by state are derived by applying national chain-type price indexes to the current dollar values of GDP by state for the 23 North American Industry Classification System-based industry sectors. The chain-type index formula that is used in the national accounts is then used to calculate the values of total real GDP by state and real GDP by state at more aggregated industry levels. Real GDP by state may reflect a substantial volume of output that is sold to other states and countries. To the extent that a state's output is produced and sold in national markets at relatively uniform prices (or sold locally at national prices), real GDP by state captures the differences across states that reflect the relative differences in the mix of goods and services that the states produce. However, real GDP by state does not capture geographic differences in the prices of goods and services that are produced and sold locally.

BEA regions

BEA groups all 50 states and the District of Columbia into 8 distinct regions for purposes of presentation and analysis as follows:

New England (Connecticut, Maine, Massachusetts, New Hampshire, Rhode Island, and Vermont) Mideast (Delaware, District of Columbia, Maryland, New Jersey, New York, and Pennsylvania) Great Lakes (Illinois, Indiana, Michigan, Ohio, and Wisconsin) Plains (Iowa, Kansas, Minnesota, Missouri, Nebraska, North Dakota, and South Dakota) Southeast (Alabama, Arkansas, Florida, Georgia, Kentucky, Louisiana, Mississippi, North Carolina, South Carolina, Tennessee, Virginia, and West Virginia) Southwest (Arizona, New Mexico, Oklahoma, and Texas) Rocky Mountain (Colorado, Idaho, Montana, Utah, and Wyoming) Far West (Alaska, California, Hawaii, Nevada, Oregon, and Washington)

Uses of GDP and personal income by state statistics

GDP and personal income by state statistics provide a framework for analyzing current economic conditions in each state and can serve as a basis for decision-making. For example:

• Federal government agencies use the statistics in forecasting models to project energy and water use. The statistics are also used as a basis for allocating funds and determining matching grants to states.
• State governments use the statistics to project tax revenues and the need for public services.
• Academic regional economists use the statistics for applied research.
• Businesses, trade associations, and labor organizations use the statistics for market research.

1.1 Definitions of Statistics, Probability, and Key Terms

For each of the following situations, indicate whether it would be best modeled with a mathematical model or a statistical model. Explain your answers.

• driving time from New York to Florida
• departure time of a commuter train at rush hour
• distance from your house to school
• temperature of a refrigerator at any given time
• weight of a bag of rice at the store

For each of the following eight exercises, identify: a. the population, b. the sample, c. the parameter, d. the statistic, e. the variable, and f. the data. Give examples where appropriate.

A fitness center is interested in the mean amount of time a client exercises in the center each week.

Ski resorts are interested in the mean age that children take their first ski and snowboard lessons. They need this information to plan their ski classes optimally.

A cardiologist is interested in the mean recovery period of her patients who have had heart attacks.

Insurance companies are interested in the mean health costs each year of their clients, so that they can determine the costs of health insurance.

A politician is interested in the proportion of voters in his district who think he is doing a new good job.

A marriage counselor is interested in the proportion of clients she counsels who stay married.

Political pollsters may be interested in the proportion of people who will vote for a particular cause.

A marketing company is interested in the proportion of people who will buy a particular product.

Use the following information to answer the next three exercises: A Lake Tahoe Community College instructor is interested in the mean number of days Lake Tahoe Community College math students are absent from class during a quarter.

What is the population she is interested in?

• all Lake Tahoe Community College students
• all Lake Tahoe Community College English students
• all Lake Tahoe Community College students in her classes
• all Lake Tahoe Community College math students

Consider the following

X X = number of days a Lake Tahoe Community College math student is absent.

In this case, X is an example of which of the following?

The instructor’s sample produces a mean number of days absent of 3.5 days. This value is an example of which of the following?

1.2 Data, Sampling, and Variation in Data and Sampling

For the following exercises, identify the type of data that would be used to describe a response (quantitative discrete, quantitative continuous, or qualitative), and give an example of the data.

number of tickets sold to a concert

percent of body fat

favorite baseball team

time in line to buy groceries

number of students enrolled at Evergreen Valley College

most-watched television show

brand of toothpaste

distance to the closest movie theatre

age of executives in Fortune 500 companies

number of competing computer spreadsheet software packages

Use the following information to answer the next two exercises: A study was done to determine the age, number of times per week, and the duration (amount of time) of resident use of a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every 8th house in the neighborhood around the park was interviewed.

Number of times per week is what type of data?

• qualitative
• quantitative discrete
• quantitative continuous

Duration (amount of time) is what type of data?

Airline companies are interested in the consistency of the number of babies on each flight, so that they have adequate safety equipment. Suppose an airline conducts a survey. Over Thanksgiving weekend, it surveys six flights from Boston to Salt Lake City to determine the number of babies on the flights. It determines the amount of safety equipment needed by the result of that study.

• Using complete sentences, list three things wrong with the way the survey was conducted.
• Using complete sentences, list three ways that you would improve the survey if it were to be repeated.

Suppose you want to determine the mean number of students per statistics class in your state. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

Suppose you want to determine the mean number of cans of soda drunk each month by students in their twenties at your school. Describe a possible sampling method in three to five complete sentences. Make the description detailed.

List some practical difficulties involved in getting accurate results from a telephone survey.

List some practical difficulties involved in getting accurate results from a mailed survey.

With your classmates, brainstorm some ways you could overcome these problems if you needed to conduct a phone or mail survey.

The instructor takes her sample by gathering data on five randomly selected students from each Lake Tahoe Community College math class. The type of sampling she used is which of the following?

• cluster sampling
• stratified sampling
• simple random sampling
• convenience sampling

A study was done to determine the age, number of times per week, and the duration (amount of time) of residents using a local park in San Jose. The first house in the neighborhood around the park was selected randomly and then every eighth house in the neighborhood around the park was interviewed. The sampling method was which of the following?

• simple random

Name the sampling method used in each of the following situations:

• A woman in the airport is handing out questionnaires to travelers asking them to evaluate the airport’s service. She does not ask travelers who are hurrying through the airport with their hands full of luggage, but instead asks all travelers who are sitting near gates and not taking naps while they wait.
• A teacher wants to know if her students are doing homework, so she randomly selects rows two and five and then calls on all students in row two and all students in row five to present the solutions to homework problems to the class.
• The marketing manager for an electronics chain store wants information about the ages of its customers. Over the next two weeks, at each store location, 100 randomly selected customers are given questionnaires to fill out asking for information about age, as well as about other variables of interest.
• The librarian at a public library wants to determine what proportion of the library users are children. The librarian has a tally sheet on which she marks whether books are checked out by an adult or a child. She records this data for every fourth patron who checks out books.
• A political party wants to know the reaction of voters to a debate between the candidates. The day after the debate, the party’s polling staff calls 1,200 randomly selected phone numbers. If a registered voter answers the phone or is available to come to the phone, that registered voter is asked whom he or she intends to vote for and whether the debate changed his or her opinion of the candidates.

A random survey was conducted of 3,274 people of the microprocessor generation —people born since 1971, the year the microprocessor was invented. It was reported that 48 percent of those individuals surveyed stated that if they had $2,000 to spend, they would use it for computer equipment. Also, 66 percent of those surveyed considered themselves relatively savvy computer users.

• Do you consider the sample size large enough for a study of this type? Why or why not?
• Based on your gut feeling , do you believe the percents accurately reflect the U.S. population for those individuals born since 1971? If not, do you think the percents of the population are actually higher or lower than the sample statistics? Why? Additional information: The survey, reported by Intel Corporation, was filled out by individuals who visited the Los Angeles Convention Center to see the Smithsonian Institute's road show called “America’s Smithsonian.”
• With this additional information, do you feel that all demographic and ethnic groups were equally represented at the event? Why or why not?
• With the additional information, comment on how accurately you think the sample statistics reflect the population parameters.

The Well-Being Index is a survey that follows trends of U.S. residents on a regular basis. There are six areas of health and wellness covered in the survey: Life Evaluation, Emotional Health, Physical Health, Healthy Behavior, Work Environment, and Basic Access. Some of the questions used to measure the Index are listed below.

Identify the type of data obtained from each question used in this survey: qualitative, quantitative discrete, or quantitative continuous.

• Do you have any health problems that prevent you from doing any of the things people your age can normally do?
• During the past 30 days, for about how many days did poor health keep you from doing your usual activities?
• In the last seven days, on how many days did you exercise for 30 minutes or more?
• Do you have health insurance coverage?

In advance of the 1936 presidential election, a magazine released the results of an opinion poll predicting that the republican candidate Alf Landon would win by a large margin. The magazine sent post cards to approximately 10,000,000 prospective voters. These prospective voters were selected from the subscription list of the magazine, from automobile registration lists, from phone lists, and from club membership lists. Approximately 2,300,000 people returned the postcards.

• Think about the state of the United States in 1936. Explain why a sample chosen from magazine subscription lists, automobile registration lists, phone books, and club membership lists was not representative of the population of the United States at that time.
• What effect does the low response rate have on the reliability of the sample?
• Are these problems examples of sampling error or nonsampling error?
• During the same year, another pollster conducted a poll of 30,000 prospective voters. These researchers used a method they called quota sampling to obtain survey answers from specific subsets of the population. Quota sampling is an example of which sampling method described in this module?

Crime-related and demographic statistics for 47 US states in 1960 were collected from government agencies, including the FBI's Uniform Crime Report . One analysis of this data found a strong connection between education and crime indicating that higher levels of education in a community correspond to higher crime rates.

Which of the potential problems with samples discussed in Data, Sampling, and Variation in Data and Sampling could explain this connection?

A website that allows anyone to create and respond to polls had a question posted on April 15 which asked:

“Do you feel happy paying your taxes when members of the Obama administration are allowed to ignore their tax liabilities?” 5

As of April 25, 11 people responded to this question. Each participant answered “NO!”

Which of the potential problems with samples discussed in this module could explain this connection?

A scholarly article about response rates begins with the following quote:

“Declining contact and cooperation rates in random digit dial (RDD) national telephone surveys raise serious concerns about the validity of estimates drawn from such research.” 6

The Pew Research Center for People and the Press admits

“The percentage of people we interview—out of all we try to interview—has been declining over the past decade or more.” 7

• What are some reasons for the decline in response rate over the past decade?
• Explain why researchers are concerned with the impact of the declining response rate on public opinion polls.

1.3 Frequency, Frequency Tables, and Levels of Measurement

Fifty part-time students were asked how many courses they were taking this term. The (incomplete) results are shown below.

• Fill in the blanks in Table 1.37 .
• What percent of students take exactly two courses?
• What percent of students take one or two courses?

Sixty adults with gum disease were asked the number of times per week they used to floss before their diagnosis. The (incomplete) results are shown in Table 1.38 .

• Fill in the blanks in Table 1.38 .
• What percent of adults flossed six times per week?
• What percent flossed at most three times per week?

Nineteen immigrants to the United States were asked how many years, to the nearest year, they have lived in the United States The data are as follows: 2, 5, 7, 2, 2, 10, 20, 15, 0, 7, 0, 20, 5, 12, 15, 12, 4, 5, 10.

Table 1.39 was produced.

• Fix the errors in Table 1.39 . Also, explain how someone might have arrived at the incorrect number(s).
• Explain what is wrong with this statement: “47 percent of the people surveyed have lived in the United States for 5 years.”
• Fix the statement in b to make it correct.
• What fraction of the people surveyed have lived in the United States five or seven years?
• What fraction of the people surveyed have lived in the United States at most 12 years?
• What fraction of the people surveyed have lived in the United States fewer than 12 years?
• What fraction of the people surveyed have lived in the United States from five to 20 years, inclusive?

How much time does it take to travel to work? Table 1.40 shows the mean commute time by state for workers at least 16 years old who are not working at home. Find the mean travel time, and round off the answer properly.

A business magazine published data on the best small firms in 2012. These were firms which had been publicly traded for at least a year, have a stock price of at least $5 per share, and have reported annual revenue between $5 million and $1 billion. Table 1.41 shows the ages of the chief executive officers for the first 60 ranked firms.

• What is the frequency for CEO ages between 54 and 65?
• What percentage of CEOs are 65 years or older?
• What is the relative frequency of ages under 50?
• What is the cumulative relative frequency for CEOs younger than 55?
• Which graph shows the relative frequency and which shows the cumulative relative frequency?

Use the following information to answer the next two exercises: Table 1.42 contains data on hurricanes that have made direct hits on the United States. Between 1851-2004. A hurricane is given a strength category rating based on the minimum wind speed generated by the storm.

What is the relative frequency of direct hits that were category 4 hurricanes?

• not enough information to calculate

What is the relative frequency of direct hits that were AT MOST a category 3 storm?

1.4 Experimental Design and Ethics

How does sleep deprivation affect your ability to drive? A recent study measured the effects on 19 professional drivers. Each driver participated in two experimental sessions: one after normal sleep and one after 27 hours of total sleep deprivation. The treatments were assigned in random order. In each session, performance was measured on a variety of tasks including a driving simulation.

Use key terms from this module to describe the design of this experiment.

An advertisement for Acme Investments displays the two graphs in Figure 1.14 to show the value of Acme’s product in comparison with the Other Guy’s product. Describe the potentially misleading visual effect of these comparison graphs. How can this be corrected?

The graph in Figure 1.15 shows the number of complaints for six different airlines as reported to the U.S. Department of Transportation in February 2013. Alaska, Pinnacle, and Airtran Airlines have far fewer complaints reported than American, Delta, and United. Can we conclude that American, Delta, and United are the worst airline carriers since they have the most complaints?

An epidemiologist is studying the spread of the common cold among college students. He is interested in how the temperature of the dorm room correlates with the incidence of new infections. How can he design an observational study to answer this question? If he chooses to use surveys in his measurements, what type of questions should he include in the survey?

• 5 lastbaldeagle. Retrieved from http://www.youpolls.com/details.aspx?id=12328.
• 6 Keeter, S., et al. (2006). Gauging the impact of growing nonresponse on estimates from a national RDD telephone survey. Public Opinion Quarterly, 70 (5). Retrieved from http://hbanaszak.mjr.uw.edu.pl/TempTxt/Links/GAUGING%20THE%20IMPACT%20OF%20GROWING.pdf.
• 7 Pew Research Center. (n.d.). Frequently asked questions. Retrieved from http://www.pewresearch.org/methodology/u-s-survey-research/frequently-asked-questions/#dont-you-have-trouble-getting-people-to-answer-your-polls.

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Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute Texas Education Agency (TEA). The original material is available at: https://www.texasgateway.org/book/tea-statistics . Changes were made to the original material, including updates to art, structure, and other content updates.

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• Authors: Barbara Illowsky, Susan Dean
• Publisher/website: OpenStax
• Book title: Statistics
• Publication date: Mar 27, 2020
• Location: Houston, Texas
• Book URL: https://openstax.org/books/statistics/pages/1-introduction
• Section URL: https://openstax.org/books/statistics/pages/1-homework

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7 fast facts about the Francis Scott Key Bridge

I n Baltimore, parts of the Francis Scott Key Bridge collapsed after it was struck by a container ship early Tuesday morning, sending vehicles plunging into the dark waters below. Here are some details about the bridge and how it came to be.

Where is it located?

The Key bridge crosses over the Patapsco River, where Francis Scott Key was inspired to write the “Star Spangled Banner,” according to the Maryland Transportation Authority. “Scholars believe the span crosses within 100 yards of the site where Francis Scott Key witnessed the bombardment of Fort McHenry on the evening of Sept. 12, 1814,” according to the website . “That battle inspired Key to write the words of the Star Spangled Banner.”

How big is the port it spans?

The bridge spans a busy shipping channel. The Port of Baltimore handled a record 52.3 million tons of foreign cargo worth $80 billion in 2023, according to Maryland Governor Wes Moore’s office . The port also handled a record total of 847,158 cars and light trucks — more than any other US port for 13 consecutive years, Moore’s office said.

The Port of Baltimore “ranks first among the nation’s ports for volume of autos and light trucks, roll on/roll off heavy farm and construction machinery, imported sugar, and imported gypsum; ninth among major U.S. ports for foreign cargo handled; and ninth for total foreign cargo value,” Moore’s office said in a statement in February 2024.

When was the bridge built?

Construction began in 1972 and was completed in March 1977. The bridge opened to traffic on March 23, 1977, as an outer crossing of Baltimore Harbor and the final link in Interstate 695, also known as the Baltimore Beltway.

How big is it?

The four-lane bridge is 1.6 miles long and has a vertical clearance of 185 feet. Including roadways that connect to it, it’s nearly 11 miles long. In 2021, its annual traffic volume was 11.3 million vehicles, with an average daily volume of 31,000 vehicles. The water beneath is the bridge is approximately 50 feet deep.

What type of bridge is it?

According to the American Society of Civil Engineers , the Key bridge was also one of the longest of its kind. “The bridge itself, with a total length of 8,636 feet, is a steel arch-shaped continuous-through-truss bridge structure that combines the behaviors of an arch, truss, and cantilever,” the Civil Engineering Almanac states on the society’s website. “With a main span of 1,200 feet, it was the second longest continuous-truss bridge span in the world when constructed and remains the second longest in the United States and third in the world.”

Has it been worked on lately?

In fiscal year 2020, the state of Maryland spent $12.4 million to “rehabilitate substructure and superstructure” of the bridge, according to a report by the state’s transportation department . Another $7.9 million was spent that year to clean and paint the structural steel of the approach spans and make miscellaneous repairs.

When asked how long it might take to replace the bridge, Baltimore Mayor Brandon Scott said at a press conference Tuesday morning that it was too early to say and that the focus was on getting people out of the river.

“We shouldn’t even be having that discussion right now,” Scott said. “The discussion right now should be about the people, the souls, the lives that we’re trying to save. There will be a time to discuss about a bridge, and how we get a bridge back up, but right now there are people in the water that we have to get out, and that is the only thing we should be talking about.”

How often is the bridge inspected?

The bridge undergoes inspections every two years, and its features were found to be in satisfactory or good condition during a 2021 review, according to the Federal Highway Administration.

Christina Prignano and Jackie Kucinich of the Globe staff contributed to this report.