STAT Midterm CH. 1-13

Which of the following statements about the table of random digits are true? Select all true statements.

-Each pair of digits has chance 1/100 of being 00. -The digits 00000 are just as likely to appear as the digits 42895.

Government regulations require that institutional review boards consist of at least five people, including at least one scientist, one nonscientist, and one person from outside the institution. Most boards are larger, but many contain just one outsider. (a) Why should review boards contain at least one person who is not a scientist?

-Nonscientists can focus on the effect of the study on participants. -Nonscientists can contribute knowledge about nonscientific areas of the study.

Government regulations require that institutional review boards consist of at least five people, including at least one scientist, one nonscientist, and one person from outside the institution. Most boards are larger, but many contain just one outsider. (b) Why should review boards contain at least one outsider?

-Outsiders have no personal reasons to see a study get approved or disapproved. -Outsiders represent the opinions of a potential participant.

According to an April 2018 survey, a majority of employed American adults (59%) are confident about their job security, stating it is not at all likely for them to lose their job or be laid off in the next 12 months. The survey methods section of the poll states that for results based on the total sample of employed adults, the margin of sampling error is ±5 percentage points at the 95% confidence level. All reported margins of sampling error include computed design effects for weighting. Identify the sources of error in the poll result that are not included in the margin of error.

-Undercoverage -Response errors -Nonresponse -Inclusion errors -Processing errors

The Ministry of Health in the Canadian province of Ontario wants to know whether the national health care system is achieving its goals in the province. Much information about health care comes from patient records, but that source does not allow to compare people who use health services with those who do not. So the Ministry of Health conducted the Ontario Health Survey, which interviewed a random sample of 61239 people who live in the province of Ontario. Estimate the margin of error for conclusions having 95% confidence about the entire adult population of Ontario. Give your answer to three decimal places.

.004

You are writing an opinion poll question about a proposed amendment to the Constitution. You can ask if people are in favor of "changing the Constitution" or "adding to the Constitution" by approving the amendment. One of these choices of wording will produce a much higher percentage in favor. Which one? Why?

A higher percentage of people will prefer adding to the Constitution because many Americans are hesitant about changing the original constitution.

In July 2018, Green Car Reports conducted a Twitter poll and asked their readers, "Which modern electric car will be the first classic?" Of the 466 people who responded to the poll, 48% chose the Tesla Roadster. (b) Explain why the poll may give unreliable information.

A poll given over Twitter is a voluntary response sample and is likely to be biased.

Here is a small part of a data set that describes Major League Baseball players as of opening day of the 2018 season. Player Team Position Age Salary ⋮ Trout, Mike Angels Outfielder 26 34,083 Headley, Chase Padres Third base 33 13,000 Axford, John Blue Jays Pitcher 35 1500 Sabathia, C. C. Yankees Pitcher 38 10,000 ⋮ What individuals does this data set describe?

Major League Baseball players

(b) An employer asks employees to participate in a research study. Although the employer has assured employees that participation is voluntary, several employees are concerned that a decision to not participate could affect performance evaluations or job advancement. Does circumstance (b) constitute coercion? Explain your reasoning.

No, because the subject is not being intentionally threatened to participate in the study.

According to the Stanford Prison Experiment website, "despite suffering extreme emotional stress during the experiment, all participants appear to have regained their baseline emotional states after the study. Extensive follow-up testing revealed no lasting trauma to participants." Does this mitigate what the subjects experienced in the experiment? Explain your reasoning.

No, the appearance of no lasting trauma does not mitigate the experience because the subjects were not informed about potential harm prior to consent and there may still be lasting trauma.

The National Health Interview Survey (NHIS) telephone survey is conducted annually in the United States. Of the first 100 numbers dialed, 55 numbers were for wireless telephones. This is not surprising, because, as of the second half of 2016, 50.8% of all U.S. households had only wireless telephones. Classify each of the two numbers as a parameter or a statistic.

PARAMETER: 50.8 STATISTIC: 55

Identify the population which the researchers were interested in and the variables they measured. Not all statements will be used.

POPULATION: - all women aged 50-64 VARIABLES: -amount of alcohol consumed daily -type of cancer -presence of cancer

An online store chooses an SRS of 100 customers from its list of all people who have bought something from the store in the last year. It asks those selected how satisfied they are with the store's website. If it selected two SRSs of 100 customers at the same time, the two samples would give somewhat different results. Is this variation a source of sampling error or of nonsampling error? Would the survey's announced margin of error take this source of error into account? Select the correct statement about the variation between the two samples.

This variation is a source of sampling error and the margin of error does take it into account.

An online store chooses an SRS of 100 customers from its list of all people who have bought something from the store in the last year. It asks those selected how satisfied they are with the store's website. If it selected two SRSs of 100 customers at the same time, the two samples would give somewhat different results. Is this variation a source of sampling error or of nonsampling error? Would the survey's announced margin of error take this source of error into account? Select the correct statement about the variation between the two samples.

This variation is a source of sampling error and the margin of error does take it into account.

The U.S. Department of Health and Human Services regulations for informed consent state that "An investigator shall seek such consent only under circumstances that provide the prospective subject or the representative sufficient opportunity to consider whether or not to participate and that minimize the possibility of coercion or undue influence." Coercion occurs when an overt or implicit threat of harm is intentionally presented by one person to another in order to obtain compliance. Consider the following circumstances: (a) An investigator tells a prospective subject that the subject will lose access to needed health services if they do not participate in the research. Does circumstance (a) constitute coercion? Explain your reasoning.

Yes, because the subject is being threatened with the act of losing health care if they do not comply.

A 72‑year‑old man with multiple sclerosis is hospitalized. His doctor feels he may need to be placed on a feeding tube soon to ensure adequate nourishment. He asks the patient about this in the morning and the patient agrees. However, in the evening (before the tube has been placed), the patient becomes disoriented and seems confused about his decision to have the feeding tube placed. He tells the doctor he does not want it in. The doctor revisits the question in the morning when the patient is again lucid. Unable to recall his state of mind from the previous evening, the patient again agrees to the procedure. Do you believe the patient has given informed consent to the procedure?

Yes. The patient gave the consent twice when he was lucid and only denied consent when he was confused.

Due to the rising costs of accidents, many employers have started requiring employees to take courses designed to heighten safety awareness. One company is trying to decide which one of two courses to implement. To help make a decision, ten employees selected at random take Course A, and another ten randomly selected employees take Course B. Each employee then takes the same safety test that is graded out of a possible 50 points. Based on the safety test scores, the company concluded that neither course was significantly better at heightening safety awareness. The population for this study is

all employees.

I plan to take a sample of 10 students in my introductory statistics class. Which of the following is a simple random sample?

I write the names of all the students on similar slips of paper, put the slips of paper in a box, mix them well, and draw 10 slips from the box. The 10 names drawn are my sample.

Scores on the Wechsler Adult Intelligence Scale for the 20 to 34 age group are approximately Normally distributed with mean 110 and standard deviation 15. How high must a person score to be in the top 5% of all scores? Enter your answer as a whole number.

IQ=135

Most sample surveys call residential telephone numbers at random. They do not, however, always ask their questions of the person who picks up the phone. Instead, they ask about the adults who live in the residence and choose one at random to be in the sample. Why is this a good idea? Select the correct explanation.

If people who answer the phone at the house are different from those who do not, the sample may be biased.

The stemplot shows the percentage of residents aged 18 to 44 in each of the 50 states in 2010. The stems are whole percents, and the leaves are tenths of a percent. Key: A stem of 37 and a leaf of 1 represents 37.1%. It turns out that Utah has the largest percentage 𝑝 of residents aged 18 to 44 years. What is the percentage for that state?

P= 39.7%

Explain why it is a bad idea to have the first five subjects learn from a store clerk that the price has increased to $550, the next five learn that the price has increased to $550 from the price tag on the rug, and so on. Instead, the order in which subjects are sent to the store and which scenario they will encounter (type of change and source of information about the change) should be determined randomly. Why? (c) The order of scenario exposure to each subject should be randomly determined because

Randomizing the order controls for other confounding variables such as time of day.

Which of the following statements is true of the standard deviation?

Removing an outlier will decrease the standard deviation.

A large study used records from Canada's national health care system to compare the effectiveness of two ways to treat prostate disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many patients whose doctors had chosen one or the other method. The study found that patients treated by the new method were more likely to die within eight years. Which of the following describes an experiment that could compare the two ways to treate prostate disease?

Researchers randomly assign individuals who have prostate disease to one of two treatment groups, traditional surgery or the new method that does not require surgery. The effectiveness of the treatment was measured after patients received treatment.

Height distributions generally have a predictable pattern. In a large introductory statistics class, students were asked to report their height. The histogram displays the distribution of heights, in inches, for 266 females from this class. Describe the shape, center, and variability of this distribution.

SHAPE: symmetric CENTER: b/t 65 and 67 in VARIATION: b/t 57 and 73 in

Do consumers prefer trucks, SUVs, and minivans to passenger cars? The data provided give the sales and leases of new cars and trucks (in thousands of vehicles) in the United States from 1996 to 2010. (The definition of "truck" includes SUVs and minivans.) Plot two line graphs on the same axes to compare the change in car and truck sales over time. Describe the trend that you see in the line graphs.

Sales and leases for both cars and trucks were at the highest in 1999 and 2000. Later years show an overall trend of gradually decreasing sales and leases until 2007 when the trend decreases sharply for both cars and trucks before beginning to rise again. Overall, trucks have much lower sales and leases than cars, except for the period 2002 to 2008 when truck sales and leases were only slightly higher than cars.

In the U.S. Census Bureau document America's Families and Living Arrangements: 2017, we find these data on the marital status of American women aged 15 years and older as of 2017: Make a bar graph to show the distribution of marital status, and describe what you see in this bar graph.

The height of the bar for married women is ALMOST TWICE as tall as the bar for women who were NEVER MARRIED The height of the bar for women who were divorced is ABOUT EQUAL TO the height of the bar for women who were widowed.

The table gives the salaries of the Minnesota Twins baseball team Construct a graph of the data. Based on the shape of the distribution, describe the position of the mean relative to the median.

The mean is likely greater than the median because the distribution is skewed to the right.

The median income of American households was $59,534 in 2007 and $61,372 in 2017. The top 5% of households earned $209,773 or more in 2007 and $237,034 or more in 2017. It is important to note that these amounts are in dollars of 2017 buying power, which allows us to compare the numbers directly. By what percentage did the income of top earners increase between 2007 and 2017? How does this compare with the percentage increase in the median household income between 2007 and 2017?

The median income for the top 5% of wage earners INCREASED BY 13% and the median income for all households INCREASED BY 3% from 2007 to 2017.

Seattle Magazine reports that the average income of its readers is $240,000. Is the median wealth of these readers greater or less than $240,000? Why?

The median is less than $240,000 because average income is inflated by the relatively few number of individuals who have much higher incomes than average.

Which of the following is an incorrect statement?

The median is the balance point in a density curve.

According to the National Household Survey on Drug Use and Health, when asked in 2016, 23.5% of those aged 18 to 25 years used cigarettes in the past month, 5.2% used smokeless tobacco, 23.2% used illicit drugs, and 38.4% engaged in binge alcohol drinking. Explain why it is not correct to display these data in a pie chart.

The percentages do not represent parts of a whole.

The host of a local radio talk show wonders if people who are actively religious are more likely to trust their neighbors than those who are not. The station receives calls from 51 listeners who voice their opinions. Identify the population.

The population is all people.

A sociologist is interested in determining what proportion of teens believe the drinking age should be lowered to 18 in all the states. The sociologist selects a sample of five high schools in a large city and interviews all 12th- graders in each of the schools. Identify the population.

The population is all teens in the U.S.

The stemplot shows IQ scores that are consistent with the 2018 article "Flynn effect and its reversal are both environmentally caused." This distribution is very close to Normal with mean 100 and standard deviation 10. Use the Normal distribution with mean 100 and standard deviation 10 as a description of the IQ scores of all adults. Use this distribution and the 68‑95‑99.7 rule to answer the questions. None of the 80 adults in our sample had scores this low. Your instructor wondered if students were surprised by that fact. Imagine that you are discussing this with a classmate, who says, "There must have been something wrong with the sample. 2.5% of 80 is 2, so I would expect to see two people in the sample with IQ's less than 80. " What is the best response to the classmate?

The sample was random, so not all samples will have the same number of people with IQ's less than 80. Since 0 and 2 are pretty close together, it is not very unusual for a random sample to have no one with an IQ less than 80

A clinical trial is

an experiment to study the effectiveness of medical treatments on actual patients.

Researchers at the University of Nevada, Las Vegas (UNLV) studied whether the attractiveness of an instructor affected the performance of students. The researchers randomly assigned 131 UNLV students to one of several instructors. Students listened to a recording of an introductory physics lecture by their instructor, and each instructor delivered the same lecture. During the lecture, the students were shown different sets of photographs, which they were told were images of the instructor. Some of the photographed people were good-looking, others less so. Students were quizzed after the lecture, and those with instructors deemed attractive performed better than those with unattractive instructors. Which of the following is true about the study and participants?

This is an experiment, and participants were randomly assigned to treatments (instructors).

Three landmarks of baseball achievement are Ty Cobb's batting average of 0.420 in 1911, Ted Williams' 0.406 in 1941, and George Brett's 0.390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and, except for outliers such as Cobb, Williams, and Brett, reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: Compute the standard scores for the batting averages of Cobb, Williams, and Brett to compare how far each stood above his peers. Enter your answers to two decimal places.

Ty Cobb's standard score: 4.15 Ted Williams' standard score: 4.26 George Brett's standard score:4.07

(b) Is the type of tweet (liberal or conservative) a treatment variable or a block? Why?

Type of tweet is a treatment variable because it can be randomly assigned to the participants, after blocking.

Each year, Forbes magazine ranks the 2000 largest metropolitan areas in the United States in an article on the best places for businesses and careers. First place in 2017 went to Portland, Oregon. Portland was ranked 5th in 2016. Fourth place in 2017 went to Denver, Colorado. Denver was ranked 1st in 2016. At the other end, York, Pennsylvania ranked 179th in 2017, up 15 spots from 194th in 2016! Are these facts evidence that Forbes's ratings are invalid, biased, or unreliable?

Unbiased

A website is looking for volunteers for a research study involving methicillin‑resistant Staphylococcus aureus (MRSA), a bacterial infection that is highly resistant to some antibiotics. The website contains the following information about the study. "The Alliance for the Prudent Use of Antibiotics is looking for individuals who have or have had MRSA to fill out an anonymous survey and provide suggestions on how to improve treatment. The survey will help us to find out more about the concerns of people affected by MRSA..." Following the announcement is a web link that takes you to the questionnaire. Does this study really provide anonymity or just confidentiality?

Websites can read your IP address and in many cases, can get your identity from it. Users would have to trust that the Alliance would keep their identities anonymous.

To explore the effects of multivitamin supplements on health, you recruit 100 volunteers. Half are to take a multivitamin supplement daily. The other half are to take a placebo daily. Multivitamin supplements may have different effects on men and women because their nutritional needs may differ. Forty of the volunteers are women and 60 are men, so you separately randomly assign half the women to the multivitamin group and half the men to the multivitamin group. The remaining volunteers are assigned to the placebo group. This is an example of

a block design but not matched pairs.

To study the effect of prayer on healing, patients with health problems are randomly divided into two groups. In one group, intercessors pray for the health of the patients. In the other group, the patients are not prayed for. The patients do not know that they are being prayed for, and the people who are praying do not come in contact with the patients for whom they pray. Medical outcomes in the two groups of patients are compared. Finally, the medical treatment team is also blind to the prayer group status of individual patients. This experiment is an example of

a double‑blind experiment

The stemplot shows the percentage of residents aged 18 to 44 in each of the 50 states in 2010. The stems are whole percents, and the leaves are tenths of a percent. Describe the shape, center, and variability of this distribution.

The shape is roughly symmetric. The center is around 35.9%. The variability is 32.5% to 39.7%.

On July 25 to 26, 1979, 42.00 inches of rain fell on Alvin, Texas. That's the most rain ever recorded in Texas for a 24-hour period. The table gives the maximum precipitation ever recorded in 24-hours (through 2010) at any weather station in each state. The record amount varies a great deal from state to state-hurricanes bring extreme rains on the Atlantic coast, and the mountain West is generally dry. Make a graph to display the distribution of records for the states. Mark where your state lies in this distribution. Briefly describe the distribution in terms of shape, center, and variability.

The shape is skewed right with a center around 13. The minimum is 5.08 and the maximum is 42.00.

The graph is a stemplot of the percentage of residents aged 18 to 44 in each of the 50 states. The stems are whole percents and the leaves are tenths of a percent. The shape of the distribution suggests that the mean will be about the same as the median. Why?

The shape of the distribution is symmetric, so the measures of center should all be similar.

The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. The histogram of the distribution is the total returns for all 1528 common stocks listed on the New York Stock Exchange in one year. Approximately what were the smallest and largest total returns? (This describes the variability of the distribution.)

The smallest total return is approximately:-60 The largest total return is approximately: 100

Select the best definition of a representative sample.

a subset of a statistical population that gives an unbiased representation of the entire population

On July 25 to 26, 1979, 42.00 inches of rain fell on Alvin, Texas. That's the most rain ever recorded in Texas for a 24-hour period. The table gives the maximum precipitation ever recorded in 24-hours (through 2010) at any weather station in each state. The record amount varies a great deal from state to state-hurricanes bring extreme rains on the Atlantic coast, and the mountain West is generally dry. In April 2018, it was reported that 49.69 inches of rain fell in a 24‑hour period on the island of Kauai, in Hawaii. If we change the precipitation amount for Hawaii from 38.00 inches to 49.69 inches, how does this impact the distribution of records for the states? In other words, would your description of shape, center, and variability need to be modified? Please select the best answer that explains the impact.

The variability will change but not the shape or center. Hawaii was already an outlier and is now the new maximum, but that does not affect the shape or center.

You are writing an opinion poll question about a proposed amendment to the Constitution. You can ask if people are in favor of "changing the Constitution" or "adding to the Constitution" by approving the amendment. Why may the responses to these two questions produce different percentages in favor?

The words "changing" and "adding" have different connotations.

One way "intelligence" can be interpreted is as "general problem‑solving ability." Explain why it is not valid to measure intelligence by a test that asks questions such as Who wrote "The Star‑Spangled Banner?" Who won the last soccer World Cup? Select the correct explanation.

These questions measure knowledge of facts rather than general problem‑solving ability.

You have the average SAT score of entering freshman for five universities. The best graphical display for these data would be a

bar graph.

In a(n) _____________, all subjects of the population are studied.

census

Government regulations require automakers to give the city and highway gas mileages for each model of car. The table gives the combined highway and city mileages (miles per gallon) for 31 model year 2015 sedans. Where is the center (the value such that half the cars have better gas mileage and half have worse gas mileage)? (Give your answer as a whole number.)

center: 27 mpg

In early 2019, several media outlets reported new statistics from the National Safety Council that revealed that, for the first time in history, Americans are more likely to die from an accidental opioid overdose than from motor vehicle crashes. According to the NSC, The odds of dying accidentally from an opioid overdose have risen to one in 96, eclipsing the odds of dying in a motor vehicle crash (one in 103). Should you be worried about your chance of dying in a motor vehicle accident this year? To answer this question, use the facts that there are about 327 million people in the United States and there are about 48000 motor vehicle deaths per year. What is the chance a typical person will die in a motor vehicle accident this year? Give your answer as a percentage rounded to three decimal places.

chance of dying: 0.015

Suppose that resting pulse rates for healthy adults are found to follow a Normal distribution, with a mean of 69 beats per minute and a standard deviation of 9.5 beats per minutes. If Bonnie has a pulse rate of 78.5 beats per minute, this means that

approximately 16% of adults have pulse rates higher than Bonnie's.

A report on the problem of vacation cruise ships polluting the sea by dumping garbage overboard said: On a seven‑day cruise, a medium‑size ship (about 1,000 passengers) might accumulate 222,000 coffee cups, 72,000 soda cans, 40,000 beer cans and bottles, and 11,000 wine bottles. Are these numbers plausible? Do some arithmetic to back up your conclusion. Suppose, for example, that the crew is as large as the passenger list. Compute the average number of cups of coffee, cans of soda, cans of beer, and bottles of wine that must be consumed per person per day. (Give your answers to one decimal place.)

average number of cups of coffee: 15.9 average number of cans of soda: 5.1 average number of cans of beer: 2.9 average number of bottles of wine: 0.8

A letter to the editor of The New York Times complained about a Times editorial that said "an American woman is beaten by her husband or boyfriend every 15 seconds." The writer of the letter claimed that "at that rate, 21 million women would be beaten by their husbands or boyfriends every year. That is simply not the case." He cited the National Crime Victimization Survey, which estimated 56,000 cases of violence against women by their husbands and 198,000 by boyfriends or former boyfriends. The survey showed 2.2 million assaults against women in all, most by strangers or someone the women knew who was not her past or present husband or boyfriend. A beating every 15 seconds is 4 beatings per minute. At that rate, how many beatings would take place in a year? Report your answer in millions of beatings, rounded to the tenth of a million. (For example, if the answer is 10,213,000 beatings, report the answer as 10.2 million.)

number of beatings in a year: 2.1 million

Westchester County is a suburban area covering 438 square miles immediately north of New York City. A garden magazine claimed that the county is home to 800,000 deer. Do a calculation that shows this claim to be implausible. (Give your answer as a whole number.)

number of deer per square mile: 1826

Government regulations require automakers to give the city and highway gas mileages for each model of car. The table gives the combined highway and city mileages (miles per gallon) for 31 model year 2015 sedans. Some of these cars are electric and the reported mileage is the electric equivalent. These cars have far higher mileage. How many electric cars are in this data set? (Give your answer as a whole number.)

number of electric cars: 5

An advantage of a stemplot over a histogram is

one can recover the actual observations from the display.

The administration of Virginia Commonwealth University (VCU) has been asked to extend the Drop/Add Period to two weeks (instead of the current one-week period). VCU will do so if it is convinced that more than half of the student body is in favor of this change. Of the 1500 students surveyed, 803 are in favor of extending the Drop/Add Period as proposed. The response variable for this study is

opinion toward proposed change.

The stemplot shows IQ scores that are consistent with the 2018 article "Flynn effect and its reversal are both environmentally caused." This distribution is very close to Normal with mean 100 and standard deviation 10. Use the Normal distribution with mean 100 and standard deviation 10 as a description of the IQ scores of all adults. Use this distribution and the 68‑95‑99.7 rule to answer the questions. What percentage 𝑝 of all students have IQ scores below 80? Give your answer as a percentage to one decimal place.

p= 2.5%

In 2018, the average performance of college‑bound seniors on the Evidence‑Based Reading and Writing (ERW) portion of the SAT followed a Normal distribution with mean 522 and standard deviation 114. The mean for the SAT Math portion was 542. What percentage 𝑝 of scores on the SAT ERW portion were lower than the SAT math mean? Give your answer to two decimal places.

p= 57.14

Organic Gardening magazine, describing how to improve your garden's soil, said, "Since a 6-inch layer of soil in a 100-square-foot plot weighs about 45,000 pounds, adding 230 pounds of compost will give you an instant 5% organic matter." Use the correct weight of 50 cubic feet of soil to determine the percent increase of organic matter in from adding 230 cubic feet of compost. Round to one decimal place.

percent increase: 6.1

An article in a midwestern newspaper about flight delays at major airports said: According to a Gannett News Service study of U.S. airlines' performance during the past five months, Chicago's O'Hare Field scheduled 114,370 flights. Nearly 10 percent, 1,136, were canceled. Check the newspaper's arithmetic. What percent of scheduled flights from O'Hare were actually canceled? (Give your answer to two decimal places.)

percent of scheduled flights: 0.99%

On February 5, 2018, the Dow Jones Industrial Average dropped 1175 points from its opening level of 25,521. This was the biggest one‑day point decline ever. By what percentage did the Dow drop that day? On October 19, 1987, the Dow Jones Industrial Average dropped 508 points from its opening level of 2245. By what percentage did the Dow drop that day? This was the biggest one‑day percentage drop ever. (Give your answers to one decimal place.)

percentage on February 5, 2018: 4.6 percentage on October 19, 1987: 22.6

The distribution of the ages of a nation's population has a strong influence on economic and social conditions. The table shows the age distribution of U.S. residents in 1950 and 2050, in millions of persons. The 1950 data come from that year's census. The 2050 data are projections made by the Census Bureau. Because the total population in 2050 is much larger than the 1950 population, comparing percentages in each age group is clearer than comparing counts. Make a table of the percentage of the total population in each age group for both 1950 and 2050. Only one age group in 1950 represents a larger percentage of the population than it does in 2050. For that age group, determine the difference of the percentages between 1950 and 2050. Report your answer to the tenth of a percent.

difference in percentages: 1.3%

Due to the rising costs of accidents, many employers have started requiring employees to take courses designed to heighten safety awareness. One company is trying to decide which one of two courses to implement. To help make a decision, ten employees selected at random take Course A, and another ten randomly selected employees take Course B. Each employee then takes the same safety test that is graded out of a possible 50 points. Based on the safety test scores, the company concluded that neither course was significantly better at heightening safety awareness. This study is a(n)

experiment.

Which of the following is not acceptable for a line graph?

having time intervals that are not equally spaced

The figure shows the behavior of a sample statistic in many samples in four situations. The heights of the bars show how often the sample statistic took various values in many samples from the same population. The true value of the population parameter is marked on each graph. Label each of the graphs in the figure as showing high or low bias and as showing high or low variability.

high bias: far from accurate low bias: on point high variable: all spread out low variable: bunched together

Between 1977 and 2017, 1465 convicted criminals were put to death in the United States. Here are data on the number of executions in several states during those years, as well as the estimated June 1, 2017, population of these states: State Population (thousands) Executions Alabama 4,875 61 Arkansas 3,004 31 Delaware 962 16 Florida 20,984 95 Indiana 6,667 20 Nevada 2,998 12 Oklahoma 3,931 112 Texas 28,305 545 Texas and Florida are among the leaders in executions. Because these are large states, we might expect them to have many executions. Find the rate of executions for each of the states just listed, in executions per million population. Because population is given in thousands, you can find the rate per million as rate per million=executionspopulation in thousands×1000 Arrange the states in order of the number of executions relative to population.

highest to lowest: OK TX DE AL AK FL NV IN

The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. The histogram of the distribution is the total returns for all 1528 common stocks listed on the New York Stock Exchange in one year. What is the approximate center of this distribution? The approximate center of this distribution

is between 15 and 20, so 18 is a good estimate.

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68-95-99.7 rule to answer the questions. How short are the shortest 16% of all pregnancies?

less than 250 days long

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68-95-99.7 rule to answer the questions. Almost all (99.7%) pregnancies fall in what range of lengths? (Give your answers as exact numbers.)

lower bound: 218 days upper bound: 314

The distribution of heights of men is approximately Normal with mean 69.2 inches and standard deviation 2.5 inches. Between which heights do the middle 95% of men fall?

lower bound: 64.2 upper bound: 74.2

Find the mean of the three numbers, 1, 2, and 15.

mean: 6

The graph is a stemplot of the percentage of residents aged 18 to 44 in each of the 50 states. The stems are whole percents and the leaves are tenths of a percent. Find the mean and the median of the data in the stemplot and verify that the mean and median are similar. Round your answers to two decimal places.

mean= 35.93 median= 35.85

The table gives the salaries of the Minnesota Twins baseball team. Find the values of the mean and the median. Round your answers to the nearest hundred thousand dollars.

mean=4300000 median=1800000

Find the median of the three numbers, 1, 2, and 15.

median: 2

Here is an excerpt from Robert Sullivan's "A Slow-Road Movement?" in the Sunday magazine section of the New York Times on June 25, 2006: In 1956, Americans drove 628 million miles; in 2002, 2.8 billion. . . . In 1997, according to the Department of Transportation, the Interstate System handled more than 1 trillion ton-miles of stuff, a feat executed by 21 million truckers driving approximately 412 billion miles. There were at least 100 million drivers in the United States in 2002. How many miles per driver per year is 2.8 billion miles? Does this seem plausible?

miles per driver: 28 no

Here is an excerpt from Robert Sullivan's "A Slow-Road Movement?" in the Sunday magazine section of the New York Times on June 25, 2006: In 1956, Americans drove 628 million miles; in 2002, 2.8 billion. . . . In 1997, according to the Department of Transportation, the Interstate System handled more than 1 trillion ton-miles of stuff, a feat executed by 21 million truckers driving approximately 412 billion miles. According to the report, on average, how many miles per year do truckers drive? Round your answer to the nearest integer. Does this seem plausible?

miles per trucker: 19619 no

Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs: 173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Make a stemplot for the number of calories in a hot dog. Construct the five‑number summary for the number of calories in hot dogs using the method from the textbook. If you use software the answer may vary, and may be incorrect.

min: 107 median: 153 max: 195

Here are the number of legal immigrants (in thousands) who settled in each state east of the Mississippi River in 2017. Construct a five number summary by hand using the method for quartiles described in the book. Do not use software. There are many different algorithms for computing the quartiles and different software implement different ones. Round to one decimal place.

minimum value: 0.8 first quartile: 3.8 median: 11 third quartile: 27.8 maximum: 139.4

The length of human pregnancies from conception to birth varies according to a distribution that is approximately Normal with mean 266 days and standard deviation 16 days. Use the 68-95-99.7 rule to answer the questions. How long are the longest 2.5% of all pregnancies? (Give your answer as an exact number.)

more than 298 days long

Many people invest in money market funds. These are mutual funds that attempt to maintain a constant price of $1 per share while paying monthly interest. The table gives the average annual interest rates (in percent) paid by all taxable money market funds from 1973 (the first full year in which such funds were available) to 2008. A plot against time may show a consistent trend underneath cycles. When did interest rates reach their overall peak during these years?

year with the peak interest rate: 1981

Use a histogram when

you want to look at the distribution of a quantitative variable.

Cut 5pieces of string having the following lengths in inches. 2.99.55.74.27.6 A subject measures the first length four times by eye. His measurements are 3.02.93.13.0 Suppose his measurements have a bias of +0.1 inches. What are the four random errors for his measurements? (Give your answers to one decimal place if necessary.) What is the variance of his four measurements?

random error 1: 0 random error 2: -0.1 random error 3: 0.1 random error 4: 0 variance: 0.0067

Professor Holmes has two teaching assistants who grade homework for a Statistics 101 course. Professor Holmes gives each of the two teaching assistants a rubric (a clear scoring guide) for the TAs to use when they grade the assignments. Holmes gives each TA the same student's paper to grade and has each TA grade the paper according to the rubric. Professor Holmes is doing this to try to guarantee the scores given by the TAs are

reliable.

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. What was the response rate for this survey? Round to one decimal place.

response rate: 4.21

There are 30 teams in the National Basketball Association (NBA) and each team has a team payroll. The team payroll consists of the total amount of money available to pay all players on the team. As an example, in the 2018‑19 season, the LA Lakers had a team payroll of $107,020,840. Suppose you were able to look at the distribution of team payrolls for all 30 teams in the NBA during the 2018‑19 season. The distribution of team payrolls should be

roughly symmetric because team payrolls are capped as part of the collective bargaining agreement to provide equality among teams.

Dejah earned $100,000 last year at her startup and wants to prepare for potential lean times. She plans to take a 20% salary decrease next year and will then take a 20% increase in the second year. One of her friends says, "That's not bad, Dejah. You will be back to your original salary in two years." Help Dejah explain to her friend that she will not be making her original salary in two years.

salary after the 20% pay cut: $80,000 salary after the 20% increase: $96,000 net change in salary: $-4,000

The distribution of heights of young men is approximately Normal with mean 69.2 inches and standard deviation 2.5 inches. What is the standard score of a height of 72 inches (6 feet)?

standard score: 1.12

For a bar graph to be accurate

the bars should have equal width.

Which of the following should you use to describe a distribution that is skewed?

the five‑number summary

A college president is interested in student satisfaction with recreational facilities on campus. A questionnaire is sent to all students and asks them to rate their satisfaction on a scale of 1 to 5 (with 5 being the best). The instrument of measurement is

the questionnaire.

If, in a study, it is not possible to determine which subjects produced which data, we would say

the subjects are anonymous.

Organic Gardening magazine, describing how to improve your garden's soil, said, "Since a 6-inch layer of soil in a 100-square-foot plot weighs about 45,000 pounds, adding 230 pounds of compost will give you an instant 5% organic matter." Determine how many times heavier soil would be compared to water if 50 cubic feet of soil weighs 45,000 pounds. Round to one decimal place.

times heavier: 14.5

The purpose of an institutional review board is

to protect the rights of human subjects (including patients) recruited to participate in research activities.

A survey was conducted and respondents were asked what color car they drive and how many miles they travel per day. Select the correct variable type for "car color" and "miles per day."

"Car color" is categorical, "miles per day" is quantitative.

Many people invest in money market funds. These are mutual funds that attempt to maintain a constant price of $1 per share while paying monthly interest. The table gives the average annual interest rates (in percent) paid by all taxable money market funds from 1973 (the first full year in which such funds were available) to 2008. Interest rates, like many economic variables, show cycles, clear but repeating up‑and‑down movements. Make a line graph of the interest paid by money market funds for these years. In which years did the interest rate cycle reach temporary peaks? (Give your answer as values of years in ascending order, separated by spaces.)

1974 1981 1984 1989 1995 2000 2007

Here are the numbers of robberies in New York City, according to the New York Police Department (NYPD), for 2000 through 2017. Display these data in a graph. What are the most important facts that the data show?

-Robberies decreased overall from 2000 to 2017, with occasional increases. -There were less than half as many robberies in 2017 than there were in 2000.

According to a June 2015 report by the Centers for Disease Control and Prevention (CDC), one in eight Americans with HIV do not know that they are infected with the virus. The night the report was released, a news station reported "1 in 8 Americans do not know that they are infected with HIV." What is wrong with the news station's reporting?

-The news station's report implies that one in eight Americans are infected with HIV. -The news station's report omitted the important piece of information that the one in eight figure is for those who are infected with HIV.

Organic Gardening magazine, describing how to improve your garden's soil, said, "Since a 6-inch layer of soil in a 100-square-foot plot weighs about 45,000 pounds, adding 230 pounds of compost will give you an instant 5% organic matter." What percent of 45,000 is 230? Round to one decimal place.

.5%

The table represents a small part of a data set that describes the fuel economy (in miles per gallon) of 2019 model motor vehicles. Make and model Vehicle type Transmission type Number of cylinders City (mpg) Highway (mpg) ⋮ BMW 430i Compact car Manual 4 21 33 Ford Flex AWD Sport utility vehicle (4WD) Automatic 6 16 22 Genesis G70 RWD Compact car Manual 4 18 28 Toyota Avalon Midsize car Automatic 6 22 31 ⋮ (a) What are the individuals in this data set?

2019 model motor vehicles

(b) Make a diagram to describe the treatments. How many treatments are there?

4

You want to choose an SRS of 20 of Indiana's 5341 voting precincts for special voting-fraud surveillance on election day. (a) To choose an SRS, how many digits would you need to make up each of your labels for the 5341 precincts? number of digits:

4

In July 2018, Green Car Reports conducted a Twitter poll and asked their readers, "Which modern electric car will be the first classic?" Of the 466 people who responded to the poll, 48% chose the Tesla Roadster. (a) What is the sample size for this poll?

466

To be in good standing at college, a student needs to maintain a certain grade point average (GPA). Typically, a student who falls below 2.0 is put on academic probation for at least a semester. At a local college, administrators wanted to increase the GPA to remain in good standing from 2.0 and reported that the anticipated increase of students on probation would be from 3% to 5% of the student body. Relatively speaking, the increase in the percentage of students at the college who would be on academic probation would be

67% over the current figure.

The average score on an exam in organic chemistry was 60. The professor gave a retest and reported that the average score on the exam increased by 25%. Calculate the average score on the retest.

75

The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. The histogram of the distribution is the total returns for all 1528 common stocks listed on the New York Stock Exchange in one year. Explain why we prefer a histogram to a stemplot for describing the returns on 1528 common stocks.

A stemplot would have too many leaves, so a histogram would make it easier to view the distribution of the data.

You read that the median income of U.S. households in 2017 was $68,145. Select the correct explanation for the term "the median income."

About half of U.S. households in 2017 had incomes higher than $68,145 and about half had incomes less than $68,145.

You are writing an article for a consumer magazine based on a survey of the magazine's readers that asked about satisfaction with mid‑priced earphones for the iPod and iPhone. Of 1648 readers who reported owning the Apple in‑ear headphone with remote and mic, 347 gave it an outstanding rating. Only 69 outstanding ratings were given by the 134 readers who owned Klipsch Image S4i earphones with microphone. Determine the proportions of respondents who ranked the Apple and Klipsch earphones as outstanding. Give your answers to two decimal places.

Apple earphones: 0.21 Klipsch earphones: 0.51

The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. The histogram of the distribution is the total returns for all 1528 common stocks listed on the New York Stock Exchange in one year. A return less than zero means that owners of the stock lost money. About what percentage of all stocks lost money?

Approximately 23% of the stocks lost money.

Some people worry about how many calories they consume. Consumer Reports magazine, in a story on hot dogs, measured the calories in 20 brands of beef hot dogs, 17 brands of meat hot dogs, and 17 brands of poultry hot dogs. Here is computer output describing the three types of hot dogs. Select the correct interpretation of the boxplots.

-If people only pay attention to what the hot dogs are made of and otherwise choose indiscriminately, then they will consume fewer calories by choosing poultry hot dogs, since on average, poultry hot dogs have fewer calories than the other two types. -There are brands of poultry hot dogs that have more calories than certain brands of beef or meat hotdogs. It is possible that someone who selects beef or meat hot dogs could consume fewer calories per hot dog than someone else who only selects poultry hot dogs.

You and your friends have probably debated who has the better cell phone operating system. You know that you are correct, but your friends insist that they are. According to Consumer Report's Cell Phones & Services 2018 report, the Samsung Galaxy Note 9 ranked first and the Apple iPhone XS Max came in second. The overall scores for the phones were 83 for the Samsung (running Android) and 82 for the iPhone (running iOS). Consumer Reports gave the edge to Samsung for handset capabilities but gave the iPhone the edge for the rear camera and the navigation system. Does this information settle the debate between you and your friends? Do you think these ratings are biased, unreliable, or both? Explain your answer. Select all statements that apply.

-It depends how the researchers in the Consumer Report collected the data. -The variables seem to be focused on cell phone features rather that the actual operating system. -The overall scores were too close to allow one to conclude that one operating system is better than the other.

To measure the effectiveness of government training programs, it is usual to compare workers' pay before and after training. But many workers sign up for training when their pay drops or they are laid off. So the "before" pay is unusually low and the pay gain looks large. Is this bias or random error in measuring the effect of a training on pay? What is a valid way to measure the success of training programs? Select all answers that apply.

-Measure the success of a training program through a test that measures skills before and after training. -This is bias because it is always overstating the effect of the government training programs.

Five Guys and In‑N‑Out Burgers are often rated among the top hamburger chains in the country. Do consumers prefer the taste of a hamburger from Five Guys or from In‑N‑Out Burgers in a blind test in which neither chain is identified? Describe the design of a matched pairs experiment to investigate this question.

-The researcher assigns each consumer to taste a hamburger at Five Guys and In‑N‑Out Burgers, randomizing the order for each consumer. The consumer rates each burger on a scale from 1 to 5. The researcher computes the average difference in ratings Five Guys minus In‑N‑Out. Neither the consumers nor the people handing out the burgers know which chain the burgers are from. -Since gender and age play a role in food preferences, subjects of the same sex and similar ages are paired together. Each subject in a pair is assigned at random to eat a burger from one of the chains. The other member of the pair eats a burger from the other chain. Neither the consumers nor the people handing out the burgers know which chain the burgers are from. The consumer rates each burger on a scale from 1 to 5. The researcher computes the average difference in ratings In‑N‑Out minus Five Guys.

Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs: Make a stemplot for the number of calories in a hot dog. The stemplot shows important facts about the distribution that the numerical summary does not tell us. What are these facts?

-The stemplot shows there are two clusters of data in the distribution. -The stemplot shows that the minimum number of calories, 107, is a low outlier.

Attitudes on same‑sex marriage have changed over time, but they also differ according to age. Figure 10.14 shows change in the attitudes on same‑sex marriage for four generational cohorts. The y‑axis in this figure shows the proportion in each generational cohort who favor same‑sex marriage. Select all statements that apply.

-There is no data displayed from 2002 for any cohort, and no data from 2001 for Millennials. -There is an increasing trend over time of people who support same‑sex marriage. -On average, a higher proportion of younger people support same‑sex marriage than older people.

Women were allowed to enter the Boston Marathon in 1972. The time (in minutes, rounded to the nearest minute) for each winning woman from 1972 to 2018 appears in table. Click on a link to download the data. Make a graph of the winning times. Give a brief description of the pattern of Boston Marathon winning times over these years. Have times stopped improving in recent years? Select all descriptions that accurately describe the line graph.

-There was a large overall decrease in winning times from 1972 until the early eighties. After the early eighties, the improvement in winning times has slowed considerably. -Winning times have generally improved slightly since the early eighties, but there has been more fluctuation recently. -Average winning times have held fairly steady since the mid nineties, although there may be a slight increase in recent years.

Informed consent should include

-consent by the subject, usually in writing. -information, in advance, about possible risks. -information, in advance, about the nature of a study.

We often see players on the sidelines of a football game inhaling oxygen. Their coaches think this will speed their recovery. We might measure recovery from intense exertion as follows: Have a football player run 100 yards three times in quick succession. Then allow three minutes to rest before running 100 yards again. Time the final run. Two experiments to investigate the effect of inhaling oxygen during the rest period can be implemented. One of the experiments is to be a completely randomized design and the other is a matched pairs design in which each subject serves as his or her own control. Suppose you have twenty football players available as subjects. For both experiments, carry out the randomization of the twenty football players to treatments as required by the design. Use Table A to carry out the randomization in both a completely randomized comparative design and a matched pairs design. Starting at line 142, determine IDs for 10 football players from the first group. Use labels 01 to 20. Enter the ID's in order as they appear in the table. Separate the ID's with commas and, if you wish, spaces,

02, 08, 17, 10, 05, 09, 19, 06, 16, 01

The heights of the bars on a relative frequency histogram displaying the lengths of rivers will add to

100 percent.

Consumer Reports magazine presented the following data on the number of calories in a hot dog for each of 17 brands of meat hot dogs: 173 191 182 190 172 147 146 139 175 136 179 153 107 195 135 140 138 Make a stemplot of the distribution of calories in meat hot dogs and briefly describe the shape of the distribution. Most brands of meat hot dogs contain a mixture of beef and pork, with up to 15% poultry allowed by government regulations. The only brand with a different makeup was Eat Slim Veal Hot Dogs. Which point on your stemplot do you think represents this brand? Which stems correspond to the two peaks on the stemplot?

107 13 amd 17

An article in a medical journal reports on an experiment to see the effect on cholesterol levels of eating three whole eggs per day compared to eating the equivalent of a yolk‑free egg substitute. The article describes the experiment as a randomized, single‑blinded experiment of 37 subjects with metabolic syndrome. (b) Why isn't a double‑blind experiment possible?

A double‑blind experiment is not possible because this would mean that BOTH THE RESEARCHERS AND SUBJECTS would NOT KNOW WHICH TREATMENT IS ADMINISTERED TO EACH SUBJECT It is not possible for THE SUBJECTS to be UNAWARE of this information

Three landmarks of baseball achievement are Ty Cobb's batting average of 0.420 in 1911, Ted Williams' 0.406 in 1941, and George Brett's 0.390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and, except for outliers such as Cobb, Williams, and Brett, reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: Which player performed better relative to his peers?

Because he has the LARGER STANDARD SCORE, MOOKIE BETTS performed better relative to his peers.

The statistics department at Cal Poly, San Luis Obispo, has 18 faculty members and 80 undergraduate majors. Use Table A, starting at line 111, to choose a stratified sample of 1 faculty member and 1 student to attend a reception being held by the university president. Begin numbering students and faculty with 01 . Enter the number corresponding to the faculty member and student chosen.

FAC MEMB: 12 STUDENT: 48

A marketing researcher wishes to study what factors affect the perceived fairness of a change in the price of an item from its advertised price. In particular, does the type of change in price (an increase or decrease) and the source of the information about the change (from a store clerk or from the price tag on the item) affect the perceived fairness? In an experiment, 20 subjects interested in purchasing a new rug are recruited. They are told that the price of a rug in a certain store was advertised at $500. Subjects are sent, one at a time, to the store, where they learn that the price has changed. Five subjects are told by a store clerk that the price has increased to $550. Five subjects learn that the price has increased to $500 from the price tag on the rug. Five subjects are told by a store clerk that the price has decreased to $450. Five subjects learn that the price has decreased to $450 from the price tag on the rug. After learning about the change in price, each subject is asked to rate the fairness of the change on a 10‑point scale with 1= "very unfair" to 10= "very fair." (a) What are the explanatory variable(s) and response variable(s) for this experiment?

EXPLANATORY: - change in rug price - info source of change RESPONSE: -subject rating on fairness of price change

A university has 30000 undergraduate and 10000 graduate students. A survey of student opinion concerning health care benefits for domestic partners of students selects 300 of the 30000 undergraduate students at random and then separately selects 100 of the 10000 graduate students at random. The 400 students chosen make up the sample. Explain why this sampling method gives each student an equal chance to be chosen. Is this a simple random sample (SRS)? Select the correct statement about the resulting sample of students.

Each undergraduate has a 300/30000=1/100 chance of being selected and each graduate student has a 100/10000=1/100 chance of being selected. Since only samples with 300 undergraduates and 100 graduate students are possible, this is not an SRS.

One characteristic of a density curve is that there is a specific total area under the curve. What is this area equal to?

Exactly 1.

We often see players on the sidelines of a football game inhaling oxygen. Their coaches think this will speed their recovery. We might measure recovery from intense exertion as follows: Have a football player run 100 yards three times in quick succession. Then allow three minutes to rest before running 100 yards again. Time the final run. Two experiments to investigate the effect of inhaling oxygen during the rest period can be implemented. One of the experiments is to be a completely randomized design and the other is a matched pairs design in which each subject serves as his or her own control. Suppose you have twenty football players available as subjects. For both experiments, carry out the randomization of the twenty football players to treatments as required by the design. Select how randomization is used in both a completely randomized comparative design and a matched pairs design.

In a completely randomized design, twenty football players are allocated at random among two treatments. 10 football players in the first group inhale oxygen during the rest period while 10 football players in the second group do not inhale oxygen during the rest period. In a matched pairs design, all 20 football players inhale oxygen during the rest period and as a separate trial do not inhale oxygen during the rest period. The order of the oxygen and no oxygen trials would be randomly assigned to each player.

The pie chart represents passenger car sales by several manufacturers in 2016. Make a bar graph of this data. What advantage does your bar graph have over the pie chart?

It is easier to compare the heights of the bars on the bar graph than it is to compare the size of the angles on the pie chart.

Three landmarks of baseball achievement are Ty Cobb's batting average of 0.420 in 1911, Ted Williams' 0.406 in 1941, and George Brett's 0.390 in 1980. These batting averages cannot be compared directly because the distribution of major league batting averages has changed over the years. The distributions are quite symmetric and, except for outliers such as Cobb, Williams, and Brett, reasonably Normal. While the mean batting average has been held roughly constant by rule changes and the balance between hitting and pitching, the standard deviation has dropped over time. Here are the facts: According to ESPN, the batting average leaders in 2018 were Mookie Betts of the Boston Red Sox for the American League (AL) and Christian Yelich of the Milwaukee Brewers for the National League (NL). Mookie Betts' batting average is 0.346 and Christian Yelich's batting average is 0.326. AL batting averages had a mean of 0.262 with standard deviation 0.0315, while NL batting averages had a mean of 0.269 with standard deviation 0.0233. Use standard scores to compare the batting averages for Betts and Yelich. Give your answer to two decimal places.

Mookie Betts' standard score: 2.67 Christian Yelich's standard score: 2.45

The side‑by‑side bar graph shows educational attainment, by sex, for those aged 25 and older. These data were collected in the 2017 Current Population Survey. Compare educational attainment for males and females.

More males than females are high school graduates or less.

According to the Stanford Prison Experiment volunteer consent form, "The nature of the research project has been fully explained to me, including, without limitation, the fact that paid volunteers will be randomly assigned to the roles of either 'prisoners' or 'guards' for the duration of the study. I understand that participation in the research project will involve a loss of privacy, that I will be expected to participate for the full duration of the study, that I will only be released from participation for reasons of health deemed adequate by the medical advisers to the research project or for other reasons deemed appropriate by Dr. Philip Zimbardo, Principal Investigator of the project, and that I will be expected to follow directions from staff members of the project or from other participants in the research project." The full consent form subjects signed can be found at http://pdf.prisonexp.org/consent.pdf. Does this meet the standards of informed consent that are outlined in this chapter? Explain your reasoning.

No, this does not meet the standards of informed consent because there is no mention of any risk of harm.

A letter to the editor of The New York Times complained about a Times editorial that said "an American woman is beaten by her husband or boyfriend every 15 seconds." The writer of the letter claimed that "at that rate, 21 million women would be beaten by their husbands or boyfriends every year. That is simply not the case." He cited the National Crime Victimization Survey, which estimated 56,000 cases of violence against women by their husbands and 198,000 by boyfriends or former boyfriends. The survey showed 2.2 million assaults against women in all, most by strangers or someone the women knew who was not her past or present husband or boyfriend. Is the letter writer correct to claim that the Times overstated the number of cases of domestic violence against women? Why or why not? Keep in mind that cases of domestic violence refer to separate cases, not separate incidents.

No, because a woman could be beaten more than once during the course of a year.

A researcher studied the number of traffic accidents that were attributed to driver fatigue at different times of the day. He noticed that the number of accidents was higher in the late afternoon (between 5 and 6 P.M.) than in the early afternoon (between 1 and 2 P.M.). He concluded that driver fatigue plays a more prominent role in traffic accidents in the late afternoon than in the early afternoon. Do you think this conclusion is justified?

No, because more drivers are on the road between 5 and 6 P.M. than between 1 and 2 P.M.

From an examination of the stemplot for residents aged 18 to 44, is it possible to determine the percentage of residents in that age range that lived in Arizona in 2010? Explain.

No, it is not possible. All the values in the stemplot are sorted by size. Only the values are included, not the states they belong to.

The mean height of men is about 69.2 inches. Women that age have a mean height of about 63.7 inches. Do you think that the distribution of heights for all adults is approximately Normal? Explain your answer.

No, it will not be Normal. Even though the distribution of each one is Normal, the means are not in the same place and the partially overlapping distributions will have two peaks.

We could measure the extent of unemployment by a count (the number of people who are unemployed) or by a rate (the percentage of the labor force that is unemployed). The number of people in the labor force grew from 122 million in September 1988, to 138 million in September 1998, to 155 million in September 2008, to 162 million in September 2018. Is the count of unemployed people a valid measure of the extent of unemployment? Explain your answer

No, the count is invalid because it does not take the changing size of the labor force into consideration.

We could measure the extent of unemployment by a count (the number of people who are unemployed) or by a rate (the percentage of the labor force that is unemployed). The number of people in the labor force grew from 122 million in September 1988, to 138 million in September 1998, to 155 million in September 2008, to 162 million in September 2018. Is the count of unemployed people a valid measure of the extent of unemployment? Explain your answer.

No, the count is invalid because it does not take the changing size of the labor force into consideration.

An article in the November 3, 2009, issue of the Guardian reported, "A separate opinion poll yesterday suggested that 50% of obese people earn less than the national average income." Income has a distribution that is such that more than 50% of all workers would earn less than the national average. Using only the information provided, is this evidence that obese people tend to earn less than other workers?

No. It is impossible to determine whether obese people tend to earn less than non-obese people without knowing the average income for both groups.

Which of the following is not a valid measurement of athletic ability?

Number of times a person goes to the gym per week.

In the U.S. Census Bureau document America's Families and Living Arrangements: 2017, we find these data on the marital status of American women aged 15 years and older as of 2017: How many women were not married in 2017?

Number of women who were not married: 65320

Do any other states stand out when you examine the rates?

OK

An article in a medical journal reports on an experiment to see the effect on cholesterol levels of eating three whole eggs per day compared to eating the equivalent of a yolk‑free egg substitute. The article describes the experiment as a randomized, single‑blinded experiment of 37 subjects with metabolic syndrome. (a) What do you think "single‑blinded" means here?

Only the researcher or the subject(s) (not both) know the treatment they are taking.

A survey of physicians found that some doctors give a placebo to a patient who complains of pain for which the physician can find no cause. If the patient's pain improves, these doctors conclude that it had no physical basis. The medical school researchers who conducted the survey claimed that these doctors do not understand the placebo effect. Why did the medical school researchers conclude that?

Placebos do work with real pain, so the placebo response tells nothing about the physical basis of the pain. In fact, placebos work poorly in hypochondriacs.

(From the news) On September 1, 2018, The Columbus Dispatch reported on a study about political polarization and social media. In this study, 901 Democrats and 751 Republicans were recruited. The Democrats were randomly divided into two groups. All were asked to follow an automated Twitter account (Twitter bot) each day for one month. One group recieved tweets with a liberal point‑of‑view, and the other tweets with a conservative point‑of‑view. Likewise, Republicans were randomly divided into two groups and recieved the same two treatments (liberal or conservative tweets). All subjects were given a test, both before and after the experiment that scored them on a liberal/conservative scale. Changes in scores were the response variable. (a) Is the political affiliation of the subjects (Democrat or Republican) a treatment variable or a block? Why?

Political affiliation is a block because participants were split on this factor initially before seeing the tweets.

Are Texas and Florida still high by this measure?

Texas is still high by this measure but Florida is not.

The distribution of the ages of a nation's population has a strong influence on economic and social conditions. The table shows the age distribution of U.S. residents in 1950 and 2050, in millions of persons. The 1950 data come from that year's census. The 2050 data are projections made by the Census Bureau. Make a histogram of the projected age distribution for the year 2050. Use the same scales as your histogram in the previous question for easy comparison. What are the most important changes in the U.S. age distribution projected for the 100-year period between 1950 and 2050?

The 2050 distribution is more uniform in the early years, and a much larger percentage survive beyond age 60 than was the case in 1950.

You are writing an article for a consumer magazine based on a survey of the magazine's readers that asked about satisfaction with mid‑priced earphones for the iPod and iPhone. Of 1648 readers who reported owning the Apple in‑ear headphone with remote and mic, 347 gave it an outstanding rating. Only 69 outstanding ratings were given by the 134 readers who owned Klipsch Image S4i earphones with microphone. What can you conclude by comparing the rates and why?

The Klipsch earphones appear to be better than the Apple earphones, but the proportion of outstanding responses may change dramatically, in either direction, with a larger sample of Klipsch respondents.

The total return on a stock is the change in its market price plus any dividend payments made. Total return is usually expressed as a percentage of the beginning price. The histogram of the distribution is the total returns for all 1528 common stocks listed on the New York Stock Exchange in one year. Describe the overall shape of the distribution of total returns.

The graph is symmetric.

Is the distribution for residents aged 18 to 44 years more or less variable than the distribution for residents aged 65 and older? Explain.

The distribution for the residents aged 65 and older is more variable because the data cover a larger range than for the distribution for residents aged 18 to 44.

Here are the number of legal immigrants (in thousands) who settled in each state east of the Mississippi River in 2017. Make a graph of the distribution. Describe its overall shape and any outliers.

The distribution is SKEWED RIGHT with TWO HIGH outliers. the FIVE NUMBER SUMMARY would be the most suitable numerical summary.

The distribution of the ages of a nation's population has a strong influence on economic and social conditions. The table shows the age distribution of U.S. residents in 1950 and 2050, in millions of persons. The 1950 data come from that year's census. The 2050 data are projections made by the Census Bureau. Make a histogram of the 1950 age distribution (in percents). Describe the main features of the distribution. In particular, describe the percentage of children relative to the rest of the population.

The distribution is right skewed. The modal class is children 10 and under. There is a sharp drop off between young children and teens.

The table gives the salaries of the players on the Minnesota Twins baseball team for the 2018 season. Make a histogram of these data. Select the correct statement about the shape, center, and spread of the distribution.

The distribution is skewed strongly to the right with center around $2 million and spread from $545,000 to $13,500,000.

Government regulations require automakers to give the city and highway gas mileages for each model of car. The table gives the combined highway and city mileages (miles per gallon) for 31 model year 2015 sedans. Make a stemplot of the combined gas mileages of these cars. What can you say about the overall shape of the distribution?

The distribution is skewed to the right.

Here are the numbers of home runs that Babe Ruth hit in his fifteen years with the New York Yankees, 1920 to 1934. 54 59 35 41 46 25 47 60 54 46 49 46 41 34 22 Make a stemplot of these data. Is the distribution roughly symmetric, clearly skewed, or neither? About how many home runs did Ruth hit in a typical year? Is his famous 60 home runs in 1927 an outlier?

The distribution is slightly skewed to the left. Because of the slight skew, the median, which is 46, is the best way to describe a typical year. Sixty home runs is not an outlier.

The quartiles of any distribution are the 25th and 75th percentiles. Interpret the meaning of the standard scores you found.

The first quartile is about 0.67 STANDARD DEVIATIONS BELOW the mean. The third quartile is 0.67 STANDARD DEVIATIONS ABOVE the mean

In the U.S. Census Bureau document America's Families and Living Arrangements: 2017, we find these data on the marital status of American women aged 15 years and older as of 2017: Would it also be correct to use a pie chart? Explain.

Yes, it would also be correct to use a pie chart because the four categories represent an entire population when combined.

In a certain town, most haircuts are between $10 and $20, but a few salons cater to high‑end clients and charge $30 to $60. The distribution of haircut prices is

skewed right.

Organic Gardening magazine, describing how to improve your garden's soil, said, "Since a 6-inch layer of soil in a 100-square-foot plot weighs about 45,000 pounds, adding 230 pounds of compost will give you an instant 5% organic matter." Water weighs about 62 pounds per cubic foot. There are 50 cubic feet in a garden layer 100 square feet in area and 6 inches deep. What would 50 cubic feet of water weigh?

weight: 3100lbs

Organic Gardening magazine, describing how to improve your garden's soil, said, "Since a 6-inch layer of soil in a 100-square-foot plot weighs about 45,000 pounds, adding 230 pounds of compost will give you an instant 5% organic matter." In fact, soil weighs about 75 pounds per cubic foot. What would 50 cubic feet of soil weigh?

weight: 3750

Does regular exercise reduce bone loss in postmenopausal women? Here are two ways to study this question. Which design will produce more trustworthy data? A researcher finds 1000 postmenopausal women who exercise regularly. She matches each with a similar postmenopausal woman who does not exercise regularly, and she follows both groups for five years. Another researcher finds 2000 postmenopausal women who are willing to participate in a study. She assigns 1000 of the women to a regular program of supervised exercise. The other 1000 continue their usual habits. The researcher follows both groups for five years. Select all statements that are true.

-The effect of a lurking variable, such as a condition that might affect someone's desire to exercise and their bone loss, is likely to be larger in 1 and less in 2 due to randomization. -1 is an observational study and 2 is an experiment.

Traumatic brain injuries (TBI) can have serious long‑term consequences, including psychiatric disorders. To determine if there is a relation between TBI and the risk of suicide, researchers examined the medical records of 7,418,391 individuals living in Denmark from 1980 to 2014. The researchers found that suicide rates were statistically significantly higher in those individuals who had medical contact for TBI compared to those without TBI. However, the medical records did not contain information about TBI suffered prior to 1977, nor did the records indicate what treatment patients with TBI received. The sample size in this study is very large, so is this good evidence that people with TBI are at greater risk for suicide than those without TBI? Select all statements that are true.

-The records did not contain information about TBI suffered prior to 1977, which will also confound the interpretation of the results. -Very large samples will yield a significant difference in treatments, even when the magnitude of the difference is small. -The greater risk of suicide for those with TBI could be due the treatment the patients received for TBI rather than the brain injury itself.

(From the news) A Washington Post article reported that psilocybin, the active ingredient of "magic mushrooms," promoted a mystical experience in two‑thirds of people who took it for the first time, according to a study published in the online journal Psychopharmacology . The authors of the article stated that their "double‑blind study evaluated the acute and longer‑term psychological effects of a high dose of psilocybin relative to a comparison compound administered under comfortable, supportive conditions." Complete the statement that correctly explains to someone who knows no statistics what the term "double‑blind" means in this experiment.

"Double‑blind" means that NEITHER THE SUBJECTS NOR RESEARCHERS knew WHETHER PSILOCYBIN OR THE COMPARISON COMPOUND WAS ADMINISTERED TO EACH SUBJECT This method prevents potential bias caused by expectations that THE SUBJECTS AND RESEARCHERS might have about WHETHER MUSHROOMS CAUSE MYSTICAL EXPERIENCES

A study, mandated by Congress when it passed No Child Left Behind in 2002, evaluated 15 reading and math software products used by 9424 students in 132 schools across the country during the 2004‑2005 school year. It is the largest study that has compared students who received the technology with those who did not, as measured by their scores on standardized tests. There were no statistically significant differences between students who used software and those who did not. Choose the meaning of "no statistically significant differences" in plain language.

The difference in scores for students who used software and those who did not is so small that it is likely to have occurred due to chance alone.

Archaeologists plan to examine a sample of two‑meter square plots near an ancient Greek city for artifacts visible in the ground. They choose separate samples of plots from floodplain, coast, foothills, and high hills. What kind of sample is this?

A stratified sample

A Washington Post article reported on a study about alcohol consumption and cancer in women. Since 1996, a team of British researchers has been gathering detailed information from 1.28 million women aged 50 to 64. The researchers recorded how much alcohol the women reported consuming when they volunteered for the study and again three years later. The researchers then examined whether there was any link with the 68775 cancers the women developed over an average of the next seven years. They found that even among women who consumed as little as 10 grams of alcohol a day on average (the equivalent of about one drink), the risk for cancer of the breast, liver, and rectum was elevated. (a) Is this an experiment?

No, because there is no treatment imposed on individuals.

Researchers tracked 2668 people from early childhood through adulthood and found that 13-year-olds who are frequent targets of bullies were three times more likely than their non‑victimized peers to be depressed later as adults. Identify the population, sample, and variables for the study. Not all statements will be used.

POPULATION: -all ppl SAMPLE: - the 2668 bullied ppl who were tracked VARIABLES: -depression -bullying (frequency, type, etc.)

(c) By June 2009, more than 10% of all the adults and children in colonies that received the placebo had had laboratory‑confirmed seasonal flu. Less than 5% of those in the colonies that received flu shots had. This difference was statistically significant. What does the term "statistically significant" mean in the context of this study?

The observed difference in the percent of adults and children who had the flu between the two groups is most likely due to the effect of the treatment, not to chance variation.

A medical researcher is interested in the rate of dementia among former NFL football players. From a list of living former players the researcher selects a sample of 20 and interviews them to determine if signs of dementia are present. Identify the population.

The population is former NFL football players.

Beginning in 2017, there was a considerable interest in the Special Counsel investigation, conducted by Robert Mueller, of possible Russian interference in the 2016 presidential election. In 2018, the Drudge Report asked its readers, "Should President Trump fire Mueller?" As of August 9, 2018, 818,628 votes had been received on the poll with 76% answering Yes to the question. This sample is certainly biased, even though the sample size is large. What is the likely direction of the bias? That is, is 76% probably higher or lower than the truth about the opinions of the population of all adults in the United States?

The sampling method used is voluntary response. It is likely that those readers of the right-leaning Drudge Report feel strongly about whether President Trump should fire Robert Mueller due to their political stance. There are likely fewer readers with an opposing political stance. As a result, the 76% from the sample is likely greater than the true percentage of the population of all adults in the United States.

A Gallup Poll conducted from February 28‑March 1, 2015, asked 1015 randomly selected adults, "How important is it that parents get their children vaccinated—extremely important, very important, somewhat important, or not at all important?" Gallup found that 54% of respondents said "extremely important." Even though 54% describes the relatively small sample of 1015 adults, compared to the 274 million adults in the United States, Gallup feels that on the basis of this one sample, they can conclude that the majority (more than 50%) of American adults feel that it is extremely important for parents to get their children vaccinated. To see why, we need to understand the variability of random samples of size 1015 drawn from the same population. In thinking about Gallup's sample of size 1015, we asked, "Could it happen that one random sample finds that 54% of adults feel that childhood vaccination is extremely important and a second random sample finds that only 42% do?" Look at the figure, which shows the results of 1000 samples of this size when the population truth is 𝑝 = 0.5, or 50%. Use the figure to support your reasoning. Would it be surprising if a sample gave 42%?

Yes, because a value of 42% is an unlikely sample proportion based on the histogram.

Researchers at UNLV studied whether the attractiveness of an instructor affected the performance of students. The researchers randomly assigned 131 UNLV students to one of several instructors. Students listened to a recording of an introductory physics lecture by their instructor, and each instructor delivered the same lecture. During the lecture, the students were shown different sets of photographs which they were told were images of the instructor. Some of the photographed people were good‑looking, others less so. Students were quizzed after the lecture, and those with instructors deemed attractive performed better than those with unattractive instructors. Which of the following is the response variable?

scores on a quiz

Imagine the situation. You go to a website to access a news story. In order to access the story, you are asked to answer a brief survey. If you choose not to answer the survey, you can only access the article for a fee. This method for obtaining a sample is an example of

voluntary response sample.

One of the most important nongovernment surveys in the United States is the General Social Survey. The GSS regularly monitors public opinion on a wide variety of political and social issues. Interviews are conducted in person in the subject's home. You may wish to visit the GSS website at http://gss.norc.org/. Are subject's responses to GSS questions anonymous, confidential, or both?

Confidential but not anonymous.

Recently, the issue of the legalization of marijuana has been appearing on more state ballots. In April 2018, a Quinnipiac University poll asked two questions about legal marijuana use. Here are the two questions: Do you think that the use of marijuana should be made legal in the United States, or not? Do you support or oppose allowing adults to legally use marijuana for medical purposes if their doctor prescribes it? One of these questions drew 63% saying the marijuana use is okay; the other drew 93% with the same response. Which wording produced the higher percentage? Why?

QUESTION 2 drew 93% in favor because A DOCTOR PRESCRIBING WEED FOR MEDICAL PURPOSES SEEMS SAFE

Government regulations require that institutional review boards consist of at least five people, including at least one scientist, one nonscientist, and one person from outside the institution. Most boards are larger, but many contain just one outsider. (c) Is one outside member enough for a review board? What are good ways to choose outside members?

No, one outside member is not enough. Choose outside members based on who most closely represents a potential participant.

Which of the following would be considered unethical in an experiment?

-Placing the interests of science over the interests of patients. -Failure to obtain informed consent from subjects. -Promising confidentiality to subjects but failing to protect it.

Due to the rising costs of accidents, many employers have started requiring employees to take courses designed to heighten safety awareness. One company is trying to decide which one of two courses to implement. To help make a decision, ten employees selected at random take Course A, and another ten randomly selected employees take Course B. Each employee then takes the same safety test that is graded out of a possible 50 points. Based on the safety test scores, the company concluded that neither course was significantly better at heightening safety awareness. In this study, safety test score is a

-numerical variable. -quantitative variable.

Due to the rising costs of accidents, many employers have started requiring employees to take courses designed to heighten safety awareness. One company is trying to decide which one of two courses to implement. To help make a decision, ten employees selected at random take Course A, and another ten randomly selected employees take Course B. Each employee then takes the same safety test that is graded out of a possible 50 points. Based on the safety test scores, the company concluded that neither course was significantly better at heightening safety awareness. The sample for this study is

20 employees.

A national survey by the Pew Research Center and USA Today, conducted between August 16 and September 12, 2016, was based on web‑based and mail responses a national sample of 4538 adults, 18 years of age or older, living in all 50 U.S. states and the District of Columbia. Those interviewed were asked to rate the job performance of police forces across the country for holding officers accountable when misconduct occurs. Possible ratings were "Excellent," "Good," "Only fair," and "Poor." Seventy percent of white respondents gave a rating of "Excellent" or "Good," while only 31% of black respondents gave a rating of ''Excellent" or "Good." For this study, which statements are true?

-A variable is the rating a respondent selected. -The individuals are the sample of 4538 adults interviewed.

Two basic types of questions are closed questions and open questions. A closed question asks the subject for one or more of a fixed set of responses. An open question allows the subject to answer in his or her own words; the interviewer writes down the responses and classifies them later. An example of an open question is What do you believe about the afterlife? An example of a closed question is What do you believe about the afterlife? Do you believe a. there is an afterlife and entrance depends only on your actions? b. there is an afterlife and entrance depends only on your beliefs? c. there is an afterlife and everyone lives there forever? d. there is no afterlife? e. I don't know. What are the advantages and disadvantages of open and closed questions?

-An advantage of closed questions is that they are easier to answer. A disadvantage of closed questions is that an individual may simplify their answer to fit a choice. -An advantage of open questions is that it allows for many different answers. A disadvantage of open questions is answers can be difficult to analyze due to unclear or vague responses.

(b) The placebo was actually the hepatitis A vaccine and that "hepatitis was not studied, but to keep the investigators from knowing which colonies received the flu vaccine, they had to offer placebo shots, and hepatitis shots do some good while sterile water injections do not." In addition, the article mentions that the colonies were studied "without the investigators being subconsciously biased by knowing which received the placebo." Which of the following is not a reason why it is important that investigators not be subconsciously biased by knowing which received the placebo?

The investigators may choose to give the flu vaccine to the colonies that already appear healthier.

Two basic types of questions are closed questions and open questions. A closed question asks the subject for one or more of a fixed set of responses. An open question allows the subject to answer in his or her own words; the interviewer writes down the responses and classifies them later. An example of an open question is What do you believe about the afterlife? An example of a closed question is What do you believe about the afterlife? Do you believe a. there is an afterlife and entrance depends only on your actions? b. there is an afterlife and entrance depends only on your beliefs? c. there is an afterlife and everyone lives there forever? d. there is no afterlife? e. I don't know. What are the advantages and disadvantages of open and closed questions?

-An advantage of open questions is that it allows for many different answers. A disadvantage of open questions is answers can be difficult to analyze due to unclear or vague responses. -An advantage of closed questions is that they are easier to answer. A disadvantage of closed questions is that an individual may simplify their answer to fit a choice.

A large study used records from Canada's national health care system to compare the effectiveness of two ways to treat prostate disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many patients whose doctors had chosen one or the other method. The study found that patients treated by the new method were significantly more likely to die within eight years. (a) Further study of the data showed that this conclusion was wrong. The extra deaths among patients treated with the new method could be explained by lurking variables. What lurking variables might be confounded with a doctor's choice of surgical or nonsurgical treatment? For example, why might a doctor avoid assigning a patient to surgery? Choose the best explanation of the described fact.

-If a patient has a little chance to survive during an operation, a doctor might choose not to recommend surgery

A firm wants to understand the attitudes of its managers toward its system for assessing employee performance. The list of all 32 of the firm's managers is provided. Use Table A to choose five to be interviewed in detail about the performance appraisal system. Begin at line 132 to choose the five managers. Use labels 00 to 31. Label the managers in alphabetical order.

-Lukako -McTominay -Rojo -Smalling -Young

Does church attendance lengthen people's lives? One study of the effect of attendance at religious services gathered data from 2001 obituaries. The researchers measured whether the obituaries mentioned religious activities and length of life. Choose the correct statement about the study.

In this study, mention of religious activities is the explanatory variable and length of life is the response variable.

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. Use the quick method to estimate the margin of error for a random sample of size 1727. Give your answer to three decimal places.

MARGIN OF ERROR: 0.024

A Gallup Poll conducted from February 28‑March 1, 2015, asked 1015 randomly selected adults, "How important is it that parents get their children vaccinated—extremely important, very important, somewhat important, or not at all important?" Gallup found that 54% of respondents said "extremely important." Even though 54% describes the relatively small sample of 1015 adults, compared to the 274 million adults in the United States, Gallup feels that on the basis of this one sample, they can conclude that the majority (more than 50%) of American adults feel that it is extremely important for parents to get their children vaccinated. To see why, we need to understand the variability of random samples of size 1015 drawn from the same population. In thinking about Gallup's sample of size 1015, we asked, "Could it happen that one random sample finds that 54% of adults feel that childhood vaccination is extremely important and a second random sample finds that only 42% do?" Look at the figure, which shows the results of 1000 samples of this size when the population truth is 𝑝 = 0.5, or 50%. Use the figure to support your reasoning. Would it be surprising if a sample from this population gave 54%?

No, because a value of 54% is not an unlikely sample proportion based on the histogram.

A Science News article reported that according to a study conducted by researchers at the Hebrew University of Jerusalem, a high‑fat diet could reset the metabolism and prevent obesity. In the study, for 18 weeks researchers fed a group of mice a high‑fat diet on a fixed schedule (eating at the same time and for the same length of time every day). They compared these mice to three other experimental groups: one that ate a low‑fat diet on a fixed schedule, one that ate an unscheduled low‑fat diet (in the quantity and frequency of its choosing), and one that ate an unscheduled high‑fat diet. All four groups of mice gained weight throughout the experiment. However, the mice on the scheduled high‑fat diet had a lower final body weight than the mice that ate an unscheduled low‑fat diet, even though both groups consumed the same amount of calories. In addition, the mice on the scheduled high‑fat diet exhibited a unique metabolic state in which the fats they ingested were not stored, but rather utilized for energy at times when no food was available, such as between meals. Does this experiment provide good evidence that a scheduled high‑fat diet is beneficial for humans?

No, treatments that work on mice in controlled, laboratory settings might not work on humans in the real world.

According to The Independent, the final polls conducted in Great Britain prior to "Brexit" (Britain's proposed exit from the European Union (EU)) indicated that the majority of voters would vote for Britain to stay part of the EU (and thus a minority would vote to leave). For example, the final online poll conducted by Populus indicated that only 45% of voters in Britain would vote to leave the EU. When all votes were tallied for the referendum, 52% of voters in Britain voted to leave the EU. Classify each of the two numbers as a parameter or a statistic.

PARAMETER: 52 STATISTIC: 45

When the Current Population Survey asked the adults in its sample of 60,000 households if they voted in the 2016 presidential election, 56% said they had. The margin of error was less than 0.3%. In fact, only 55% of the adult population voted in that election. Give a reasonable explanation for how the CPS could choose a sample properly and still miss by 3 times the margin of error.

People who did not actually vote probably claimed that they had voted. The margin of error covers sampling errors only, not other forms of error.

When the Current Population Survey asked the adults in its sample of 60,000 households if they voted in the 2016 presidential election, 56% said they had. The margin of error was less than 0.3%. In fact, only 55% of the adult population voted in that election. Give a reasonable explanation for how the CPS could choose a sample properly and still miss by 3 times the margin of error.

People who did not actually vote probably claimed that they had voted. The margin of error covers sampling errors only, not other forms of error.

A national survey of TV network news viewers found that 48% said they would believe a phone‑in poll of 300,000 persons over a random sample of 1000 persons. Of the viewers, 42% said they would believe the random sample poll. Explain to someone who knows no statistics which choice is the better guide to what all people think.

People who feel strongly about a topic are more likely to respond to a phone‑in poll in order to voice their feelings. Random sampling ensures a proper mix of people who feel strongly and people who do not.

An optimistic account of learning online reports a study at Nova Southeastern University, Fort Lauderdale, Florida. The authors of the study claim that students taking undergraduate courses online were "equal in learning" to students taking the same courses in class. However, the Nova Southeastern University study does not tell much about Web versus classroom learning because the students who chose the Web version were much better prepared. Choose the best design of an experiment to get better information.

Students registering for a course should be randomly assigned to a classroom or online version of the course. Scores on a standardized test can then be compared.

Determine if each of the potential sample survey questions is clear or is slanted towards a desired response. (a) Which of the following best represents your opinion on gun control? The government should take away our guns. We have the right to keep and bear arms. (b) In light of skyrocketing gasoline prices, we should consider opening up a very small amount of Alaskan wilderness for oil exploration as a way of reducing our dependence on foreign oil. Do you agree or disagree? (c) Do you think that excessive restrictions placed on U.S. law enforcement agencies hampered their ability to detect the 9/11 terrorist plot before it occurred? (d) Do you use drugs?

THE QUESTION IS CLEAR: a, d THE QUESTION IS SLANTED: b, c

Just before a presidential election, a national opinion poll increases the size of its weekly random sample from the usual 1000 people to 4000 people. Does the larger random sample reduce the bias and the variability of the poll result?

The larger sample reduces variability but not bias. Both samples are unbiased because random sampling was used.

An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address. One of the survey results was that 33% of mothers communicate at least once a day with their child while at school. Do you think that the margin of error is a good measure of the accuracy of the survey's results? Explain your answer.

The margin of error is not a good measure of the accuracy of the survey's results because of undercoverage in the sampling frame.

Though opinion polls usually make 95% confidence statements, some sample surveys use other confidence levels. The monthly unemployment rate, for example, is based on the Current Population Survey of about 60,000 households. The margin of error in the unemployment rate is announced as about two‑tenths of one percentage point with 90% confidence. Would the margin of error for 95% confidence be smaller or larger? Why?

The margin of error would be larger because the cost of higher confidence is a larger margin of error.

A press release by the Gallup News Service states that, based on a poll conducted on October 5‑11, 2017, it found that 55% of Americans respond Yes when asked this question: "Are you in favor of the death penalty for a person convicted of murder?" Toward the end of the article, you read: "Results for this Gallup poll are based on telephone interviews conducted Oct. 5‑11, 2017, with a random sample of 1028 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia." What population do you think Gallup wants information about? What was the sample?

The population is all adults, 18 years of age or older, living in all 50 U.S. states and the District of Columbia, and the sample is the 1028 adults who had telephone interviews.

A national survey by the Pew Research Center and USA Today, conducted from August 16 to September 12, 2016, was based on web-based and mail responses from a national sample of 4538 adults, 18 years of age or older, living in all 50 U.S. states and the District of Columbia. Those interviewed were asked to rate the job performance of police forces across the country for holding officers accountable when misconduct occurs. Possible ratings were "Excellent," "Good," "Only fair," and "Poor." Seventy percent of white respondents gave a rating of "Excellent" or "Good," while only 31% of black respondents gave a rating of "Excellent" or "Good." What is the population and sample for this Pew research study?

The population is all adults, 18 years of age or older, living in all 50 U.S. states and the District of Columbia, and the sample is the 4538 adults who provided responses.

Is the following question slanted toward a desired response? If so, how? In view of escalating environmental degradation and incipient resource depletion, would you favor economic incentives for recycling of resource‑intensive consumer goods? Please select the correct answer.

The question is slanted. The part of the question "In view of escalating environmental degradation and incipient resource depletion" leads the respondent to answer yes.

A large study used records from Canada's national health care system to compare the effectiveness of two ways to treat prostate disease. The two treatments are traditional surgery and a new method that does not require surgery. The records described many patients whose doctors had chosen one or the other method. The study found that patients treated by the new method were more likely to die within eight years. Explain why is this study an observational study, not an experiment?

The researchers observed individuals and measured variables of interest, but did not intervene in order to influence the responses.

You are the president of the neighborhood civic association. A brewpub is thinking of opening a restaurant and bar in the neighborhood. You report to the members of the civic association that 91 emails have been received on the issue, of which 71 oppose opening the restaurant and bar. "I'm surprised that most of our residents oppose the restaurant and bar. I thought it would be quite popular," says a member of the association. Which is the most likely reason for the results of the emails to differ from the opinions of the general public?

The sample is not representative of the general thinking of the public due to voluntary response bias.

Beginning in 2017, there was a considerable interest in the Special Counsel investigation, conducted by Robert Mueller, of possible Russian interference in the 2016 presidential election. In 2018, the Drudge Report asked its readers, "Should President Trump fire Mueller?" As of August 9, 2018, 818,628 votes had been received on the poll with 76% answering Yes to the question. This sample is certainly biased, even though the sample size is large. What is the likely direction of the bias? That is, is 76% probably higher or lower than the truth about the opinions of the population of all adults in the United States?

The sampling method used is voluntary response. It is likely that those readers of the right-leaning Drudge Report feel strongly about whether President Trump should fire Robert Mueller due to their political stance. There are likely fewer readers with an opposing political stance. As a result, the 76% from the sample is likely greater than the true percentage of the population of all adults in the United States.

There may be a "gender gap" in political party preference in the United States, with women more likely than men to prefer Democratic candidates. A political scientist interviews a large sample of registered voters, both men and women. She asks each voter whether he or she voted for the Democratic or the Republican candidate in the last presidential election. Complete the following sentences.

The study IS NOT an experiment because THERE IS NO TREATMENT IMPOSED ON INDIVIDUALS The explanatory variable is GENDER and the response variable is POLITICAL PARTY PREFERENCE

Consider two at‑home tests for HIV. The first is a swab of your gums that gives you results in 20 minutes. Another at‑home HIV‑test has you prick your finger to get a small amount of blood. You mail your blood sample to a lab and get your results in about a week. Your name is not on the test, so you can find out the result by ID number. With both of these at‑home HIV tests, nothing is reported to your insurance or placed in your medical records.

The swab test offers ANONYMITY BUT NOT CONFIDENTIALITY. The blood sample test offers CONFIDENTIALITY BUT NOT ANONYMITY

Researchers from Yale University, working with medical teams in Tanzania, wanted to know how common infection with the AIDS virus is among pregnant women in that African country. To do this, they planned to test blood samples drawn from pregnant women. Yale's institutional review board insisted that the researchers get the informed consent of each woman and tell her the results of the test. This is the usual procedure in developed nations. The Tanzanian government did not want to tell the women why blood was drawn or tell them the test results. The government feared panic if many people turned out to have an incurable disease for which the country's medical system could not provide care. The study was canceled. Why was Yale justified in applying its usual standards for protecting individuals?

The women in the study have a right to be informed about the nature of the study.

Choosing at random is a "fair" way to decide who gets some scarce good, in the sense that everyone has the same chance to win. But random choice is not always a good idea — sometimes we do not want to treat everyone the same because some people have a better claim. There are three different situations. Tickets. The basketball arena has 4000 student seats, and 7000 students want tickets. Livers. The list of people waiting for liver transplants is much larger than the number of available livers. Army. During the Vietnam War, young men were chosen for army service at random, by a "draft lottery". Decide if a random selection is the best way to choose a person in the given situations.

USE RANDOM CHANCE: -Tickets DO NOT USE RANDOM CHANCE: -livers -army

A press release by the Gallup News Service states that, based on a poll conducted on October 5‑11, 2017, it found that 55% of Americans respond Yes when asked this question: "Are you in favor of the death penalty for a person convicted of murder?" Toward the end of the article, you read: "Results for this Gallup poll are based on telephone interviews conducted Oct. 5‑11, 2017, with a random sample of 1028 adults, aged 18 and older, living in all 50 U.S. states and the District of Columbia." What variable did this poll measure?

Whether or not an individual is in favor of the death penalty for a person convicted of murder.

The Community Intervention Trial for Smoking Cessation asked whether a community‑wide advertising campaign would reduce smoking. The researchers located 11 pairs of communities, with each pair similar in location, size, economic status, and so on. One community in each pair was chosen at random to participate in the advertising campaign and the other was not. Select the description that most accurately describes the design of the smoking reduction analysis.

a matched pairs experiment

A(n) _____________ is a single subject or object to be measured or studied

individual

A method for selecting a sample is said to be biased if

it systematically favors certain outcomes.

In October 2017, the Gallup Poll asked a sample of 1028 U.S. adults, "Are you in favor of the death penalty for a person convicted of murder?" Suppose that the margin of error needs to be half as large for this poll. How many people must be interviewed? Note that the size of the new sample is denoted by 𝑛. Give your answer as a whole or exact number.

n= 4112

You want to choose an SRS of 20 of Indiana's 5341 voting precincts for special voting-fraud surveillance on election day. (b) Use the table at line 107 to choose the SRS, and list the first four labels of the precincts you selected.

precincts 94, 3831, 4893, and 720

When a margin of error is reported for a survey, it includes

random sampling error, but not other practical difficulties like undercoverage and nonresponse.

Researchers recruited 60 undergraduate students, in exchange for course credit, for a study on the effect of recycling on how much wrapping paper subjects used to wrap a gift. The subjects were randomly assigned to one of two rooms. In one room there was a large recycling bin and in the other a large trash bin. The subjects were asked to wrap a gift. Unknown to the students, the researchers were interested in how much paper the students used. The researchers found that the students in the room with the recycling bin used (statistically) significantly more paper than those in the room with a trash bin. The researchers hypothesized that people, in general, would rather recycle than trash, and hence will use less disposable resources when recycling is not available. In this experiment, the amount of wrapping paper used is

the response variable.

A club has 30 student members and 10 faculty members. The students are Student Members Aguirre Cooper Kemp Peralta Stankiewicz Butterfield Dobbs Kessler Risser Steele Caporuscio Freeman Koepnick Rodriguez Tong Carlson Girard Macha Ryndak White Chilson Gonzales Makis Soria Williams Clement Grebe Palacios Spiel Zhang The faculty members are Faculty Members Atchade Everson Hansen Nair Romero Craigmile Fink Murphy Nguyen Turkmen The club can send 3 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. What is the chance, 𝑃(White), that the student named White is chosen? Give your answer as a percentage rounded to the nearest whole number. What is the chance, 𝑃(Romero), that the faculty member Romero is chosen? Give your answer as a percentage rounded to the nearest whole number.

𝑃(White)= 3 𝑃(Romero)= 10