Introductory Statistics Exploring The World Through Data 3rd Edition Robert Gould, Rebecca Wong, Colleen N. Ryan - Solutions

Go back to the information in exercise 11.20. Assuming the conditions for ANOVA are met, test the hypothesis that the mean number of hours of TV varies by class, reporting the p value and conclusion. Use the 0.05 level of significance. State your conclusion in the context of the data.Exercise
Go back to the information in exercise 11.19. Assuming the conditions for ANOVA are met, test the hypothesis that the mean number of hours of schoolwork varies by class, reporting the p-value and conclusion. Use the 0.05 level of significance. State your conclusion in the context of the
The following table shows the number of hits for a random sample of Major League Baseball players two months into the season. The table shows data for samples of three positions: shortstop, left field, and first base.a. Compare the sample mean number of hits for the three positions.b. Find the
Use the data from exercise 11.8 and find Bonferroni-corrected intervals for all three comparisons assuming an overall confidence level of 95%, using an individual confidence level of 98.33%. Then state whether the means are significantly different based on whether the intervals capture 0 or not.
Use the data from exercise 11.7 and find Bonferroni-corrected intervals for all three comparisons assuming an overall confidence level of 95%, that is, an individual confidence level of 98.33%. Then state whether the means are significantly different based on whether the intervals capture 0 or not.
The following table shows the least expensive gas prices for three cities on June 1, 2018, as reported by Gasbuddy.com.a. Assuming the overall level of significance is 0.05, what is the Bonferroni-correct level of significance for the three pairs of cities?b. Report the sample mean for each city.
The website Gasbuddy.com reports the least expensive gas prices in some cities on a daily basis. The following table shows the least expensive gas prices for three cities on June 1, 2018.a. Assuming the overall level of significance is 0.05, what is the Bonferroni-corrected level of significance
Random samples of rents for 1-bedroom 1-bath apartments in Seattle, San Francisco, and Santa Monica were selected and shown in the following table. Use three two-sample t-tests, applying the appropriate Bonferroni Correction to achieve an overall significance level of 0.05, to compare all possible
Suppose you have four groups of data, and you want to do hypothesis tests (t-tests) to compare all possible pairs of means.a. How many pairwise comparisons can be done with four groups called A, B, C, and D? Show all possible pairs, starting with AB.b. Using the Bonferroni Correction, which
Suppose you have five groups of observations, and you do hypothesis tests (t-tests) to compare all possible pairs of means.a. How many pairwise comparisons can be done with five groups? List all comparisons with five groups labeled A, B, C, D, and E, starting with AB, AC, and so on.b. Using the
a. You want to test whether an association exists between two categorical variables. For example, you want to test whether there is an association between belief in global warming and political party affiliation.b. You want to test whether the sample mean of a numerical variable is different from
a. You want to test whether there is an association between a categorical variable and a numerical variable. For example, you want to test whether there is an association between type of apartment (studio, one-bedroom, or two-bedroom) and monthly rent.b. You want to test whether the means of a
A study is done to see whether a coin is biased. The alternative hypothesis used is two sided, and the obtained z-value is 2. Assuming that the sample size is sufficiently large and that the other conditions are also satisfied, use the Empirical Rule to approximate the p-value.
A study is done to see whether a coin is biased. The alternative hypothesis used is two sided, and the obtained z-value is 1. Assuming that the sample size is sufficiently large and that the other conditions are also satisfied, use the Empirical Rule to approximate the p-value.
A researcher studying extrasensory perception (ESP) tests 300 students. Each student is asked to predict the outcome of a large number of coin flips. For each student, a hypothesis test using a 5% significance level is performed. If the p-value is less than or equal to 0.05, the researcher
Suppose you tested 50 coins by flipping each of them many times. For each coin, you perform a significance test with a significance level of 0.05 to determine whether the coin is biased. Assuming that none of the coins is biased, about how many of the 50 coins would you expect to appear biased when
The 2018 Pew Research poll in exercise 10.43 also reported responses by political party. Survey results found 45% of Republicans and 69% of Democrats supported marijuana legalization.a. Use these results to fill in the following two-way table with the counts in each category. Assume the sample size
In 2016 a Harris poll estimated that 3.3% of American adults are vegetarian. A nutritionist thinks this rate has increased and will take a random sample of American adults and record whether or not they are vegetarian. State the null and alternative hypotheses in words and in symbols.
A college chemistry instructor thinks the use of embedded tutors (tutors who work with students during regular class meeting times) will improve the success rate in introductory chemistry courses. The passing rate for introductory chemistry is 62%. The instructor will use embedded tutors in all
According to a 2015 University of Michigan poll, 71.5% of high school seniors in the United States had a driver’s license. A sociologist thinks this rate has declined. The sociologist surveys 500 randomly selected high school seniors and finds that 350 have a driver’s license.a. Pick the
In 2016, the Centers for Disease Control and Prevention estimated that the flu vaccine was 73% effective against the influenza B virus. An immunologist suspects that the current flu vaccine is less effective against this virus. Pick the correct pair of hypotheses the immunologist could use to test
The National Association for Law Placement estimated that 86.7% of law school graduates in 2015 found employment. An economist thinks the current employment rate for law school graduates is different from the 2015 rate. Pick the correct pair of hypotheses the economist could use to test this
A manager at a casual dining restaurant noted that 15% of customers ordered soda with their meal. In an effort to increase soda sales, the restaurant begins offering free refills with every soda order for a two-week trial period. During this trial period, 17% of customers ordered soda with their
The label on a can of mixed nuts says that the mixture contains 40% peanuts. After opening a can of nuts and finding 22 peanuts in a can of 50 nuts, a consumer thinks the proportion of peanuts in the mixture differs from 40%. The consumer writes these hypotheses: H0: p ≠ 0.40 and Ha: p = 0.44
An immunologist is testing the hypothesis that the current flu vaccine is less than 73% effective against the flu virus. The immunologist is using a 1% significance level and these hypotheses: Ho: p = 0.73 and Ha: p < 0.73. Explain what the 1% significance level means in context.
An economist is testing the hypothesis that the employment rate for law school graduates is different from 86.7%. The economist is using a 5% significance level and these hypotheses: H0: p = 0.867 and Ha: p ≠ 0.867. Explain what the 5% significance level means in context.
According to a 2017 Pew Research Center report, 37% of adults aged 18 to 29 had student loan debt. Suppose in a random sample of adults from this age group 48 out of 120 had student loan debt.a. Give the null and alternative hypotheses to test that the student loan rate is not 37%.b. Report the
According to Green Car Reports, 4.4% of cars sold in California in 2017 were hybrid cars. Suppose in a random sample of 500 recently sold cars in California 18 were hybrid.a. Write the null and alternative hypotheses to test that hybrid car sales in California have declined.b. Report the value of
In 2016 the Harris poll estimated that 3.3% of American adults are vegetarian. A nutritionist thinks this rate has increased. The nutritionist samples 150 American adults and finds that 11 are vegetarian.a. What is p̂, the sample proportion of vegetarians?b. What is p0, the hypothetical proportion
A college chemistry instructor thinks the use of embedded tutors will improve the success rate in introductory chemistry courses. The passing rate for introductory chemistry is 62%. During one semester, 200 students were enrolled in introductory chemistry courses with an embedded tutor. Of these
St. Louis County is 24% African American. Suppose you are looking at jury pools, each with 200 members, in St. Louis County. The null hypothesis is that the probability of an African American being selected into the jury pool is 24%.a. How many African Americans would you expect on a jury pool of
A hospital readmission is an episode when a patient who has been discharged from a hospital is readmitted again within a certain period. Nationally the readmission rate for patients with pneumonia is 17%. A hospital was interested in knowing whether their readmission rate for pneumonia was less
In a Northeastern University/Gallup poll of 461 young Americans aged 18 to 35, 152 reported they would be comfortable riding in a self-driving car. Suppose we are testing the hypothesis that more than 30% of Americans in this age group would be comfortable riding in a self-driving car, using a
According to a Gallup poll, 11.55% of American adults have diabetes. Suppose a researcher wonders if the diabetes rate in her area is higher than the national rate. She surveys 150 adults in her area and finds that 21 of them have diabetes.a. If the region had the same rate of diabetes as the rest
Suppose we are testing people to see whether the rate of use of seat belts has changed from a previous value of 88%. Suppose that in our random sample of 500 people we see that 450 have the seat belt fastened. Which of the following figures has the correct p value for testing the hypothesis that
According to a 2018 survey by Timex reported in Shape magazine, 73% of Americans report working out one or more times each week. A nutritionist is interested in whether this percentage has increased. A random sample of 200 Americans found 160 reported working out one or more times each week. Carry
According to a 2017 AAA survey, 35% of Americans planned to take a family vacation (a vacation more than 50 miles from home involving two or more immediate family members. Suppose a recent survey of 300 Americans found that 115 planned on taking a family vacation. Carry out the first two steps of a
According to a 2018 survey by Timex reported in Shape magazine, 73% of Americans report working out one or more times each week. A nutritionist is interested in whether this percentage has increased. A random sample of 200 Americans found 160 reported working out one or more times each week. The
According to a 2017 AAA survey, 35% of Americans planned to take a family vacation (a vacation more than 50 miles from home involving two or more immediate family members). Suppose a recent survey of 300 Americans found that 115 planned on taking a family vacation. In Exercise 8.30 you carried out
A 2018 Gallup poll of 3635 randomly selected Facebook users found that 2472 get most of their news about world events on Facebook. Research done in 2013 found that only 47% of all Facebook users reported getting their news about world events on Facebook. See page 430 for guidance.a. Does this
A 2018 Gallup poll of 2228 randomly selected U.S. adults found that 39% planned to watch at least a “fair amount” of the 2018 Winter Olympics. In 2014, 46% of U.S. adults reported planning to watch at least a “fair amount.”a. Does this sample give evidence that the proportion of U.S. adults
Historically (from about 2001 to 2014), 57% of Americans believed that global warming is caused by human activities. A March 2017 Gallup poll of a random sample of 1018 Americans found that 692 believed that global warming is caused by human activities.a. What percentage of the sample believed
Suppose a poll is taken that shows 220 out of 400 randomly selected Twitter users feel that Twitter should do more to decrease hateful and abusive content on the site. Test the hypothesis that the majority (more than 50%) of Twitter users feel the site should do more to decrease hateful and abusive
According to the Brookings Institution, 50% of eligible 18- to 29-year-old voters voted in the 2016 election. Suppose we were interested in whether the proportion of voters in this age group who voted in the 2018 election was higher. Describe the two types of errors we might make in conducting this
What superpower do Americans want most? In past years, 10% of Americans chose invisibility as the most desired superpower, based on the Marist poll. Assume this is an accurate representation of all Americans. A group of futurists examines a more recent 2018 Marist poll that found that 12% of those
A psychologist is interested in testing whether offering students a financial incentive improves their video-game-playing skills. She collects data and performs a hypothesis test to test whether the probability of getting to the highest level of a video game is greater with a financial incentive
Is it acceptable practice to look at your research results, note the direction of the difference, and then make the alternative hypothesis one-sided in order to achieve a significant difference? Explain.
If we reject the null hypothesis, can we claim to have proved that the null hypothesis is false? Why or why not?
When a person stands trial for murder, the jury is instructed to assume that the defendant is innocent. Is this claim of innocence an example of a null hypothesis, or is it an example of an alternative hypothesis?
When, in a criminal court, a defendant is found “not guilty,” is the court saying with certainty that he or she is innocent? Explain.
A magazine advertisement claims that wearing a magnetized bracelet will reduce arthritis pain in those who suffer from arthritis. A medical researcher tests this claim with 233 arthritis sufferers randomly assigned either to wear a magnetized bracelet or to wear a placebo bracelet. The researcher
A weight-loss diet claims that it causes weight loss by eliminating carbohydrates (breads and starches) from the diet. To test this claim, researchers randomly assign overweight subjects to two groups. Both groups eat the same amount of calories, but one group eats almost no carbs, and the other
When comparing two sample proportions with a two-sided alternative hypothesis, all other factors being equal, will you get a smaller p-value with a larger sample size or a smaller sample size? Explain.
In a 2018 study reported in The Lancet, Molina et al. reported on a study for treatment of patients with HIV-1. The study was a randomized, controlled, double-blind study that compared the effectiveness of ritonavir-boosted darunavir (rbd), the drug currently used to treat HIV-1, with dorovirine, a
In a 2018 study reported in The Lancet, Mercie et al. investigated the efficacy and safety of varenicline for smoking cessation in people living with HIV. The study was a randomized, double-blind, placebo-controlled trial. Of the 123 subjects treated with varenicline, 18 abstained from smoking for
The researchers in a Pew study interviewed two random samples, one in 2015 and one in 2018. Both samples were asked, “Have you read a print book in the last year?” The results are shown in the table below.a. Find and compare the sample proportions that had read a print book for these two
Pew Research published survey results from two random samples. Both samples were asked, “Have you listened to an audio book in the last year?” The results are shown in the table below.a. Find and compare the sample proportions that had listened to an audio book for these two groups.b. Are a
A Gallup poll asked college students in 2016 and again in 2017 whether they believed the First Amendment guarantee of freedom of the press was secure or threatened in the country today. In 2016, 2489 out of 3072 students surveyed said that freedom of the press was secure or very secure. In 2017,
A Gallup poll asked college students in 2016 and again in 2017 whether they believed the First Amendment guarantee of freedom of religion was secure or threatened in the country today. In 2016, 2089 out of 3072 students surveyed said that freedom of religion was secure or very secure. In 2017, 1929
A Gallup poll asked a random samples of Americans in 2016 and 2018 if they were satisfied with the quality of the environment. In 2016, 543 were satisfied with the quality of the environment and 440 were dissatisfied. In 2018, 461 were satisfied and 532 were dissatisfied. Determine whether the
In 2017 the Pew Research Center conducted a survey on family-leave practices and attitudes. Respondents were asked to complete this sentence: “When a family member has a serious health condition, caregiver responsibilities . . .” with choices being “mainly on women,” “mainly on men,” or
For each of the following, state whether a one-proportion z-test or a two-proportion z test would be appropriate, and name the population(s).a. A polling agency takes a random sample of voters in California to determine if a ballot proposition will pass.b. A researcher asks a random sample of
For each of the following, state whether a one-proportion z-test or a two-proportion z test would be appropriate, and name the population(s).a. A researcher takes a random sample of voters in western states and voters in southern states to determine if there is a difference in the proportion of
A student who claims that he can tell tap water from bottled water is blindly tested with 20 trials. At each trial, tap water or bottled water is randomly chosen and presented to the student who much correctly identify the type of water. The experiment is designed so that the student will have
A student is tested to determine whether she can tell butter from margarine. She is blindfolded and given small bites of toast that has been spread with either butter or margarine that have been randomly chosen. The experiment is designed so that she will have exactly 15 bites with butter and 15
A community college used enrollment records of all students and reported that that the percentage of the student population identifying as female in 2010 was 54% whereas the proportion identifying as female in 2018 was 52%. Would it be appropriate to use this information for a hypothesis test to
A student was tested to see if he could tell the difference between two different brands of cola. He was presented with 20 samples of cola and correctly identified 12 of the samples. Since he was correct 60 percent of the time, can we conclude that he can correctly tell the difference between two
Pew Research conducts polls on social media use. In 2012, 66% of those surveyed reported using Facebook. In 2018, 76% reported using Facebook.a. Assume that both polls used samples of 100 people. Do a test to see whether the proportion of people who reported using Facebook was significantly
In the Pew Research social media survey, television viewers were asked if it would be very hard to give up watching television. In 2002, 38% responded yes. In 2018, 31% said it would be very hard to give up watching television.a. Assume that both polls used samples of 200 people. Do a test to see
Pew Research reported that in the 2016 presidential election, 53% of all male voters voted for Trump and 41% voted for Clinton. Among all women voters, 42% voted for Trump and 54% voted for Clinton. Would it be appropriate to do a two-proportion z-test to determine whether the proportions of men
According to a 2016 report by the Census Bureau, 60.1% of women and 57.6% of men have completed some college education or higher. Would it be appropriate to do a two proportion z-test to determine whether the proportions of men and women who had completed some college education or higher were
According to the Bureau of Labor Statistics, 10.1% of Americans are self-employed. A researcher wants to determine if the self-employment rate in a certain area is different. She takes a random sample of 500 working residents from the area and finds that 62 are self-employed.a. Test the hypothesis
According to a 2016 report from the Institute for College Access and Success 66% of all graduates from public colleges and universities had student loans. A public college surveyed a random sample of 400 graduates and found that 62% had student loans.a. Test the hypothesis that the percentage of
A Quinnipiac poll conducted on February 20, 2018, found that 824 people out of 1249 surveyed favored stricter gun control laws. A survey conducted one week later on February 28, 2018, by National Public Radio found that 754 out of 1005 people surveyed favored stricter gun control laws.a. Find both
A Gallup poll conducted in 2017 found that 648 out of 1011 people surveyed supported same-sex marriage. An NBC News/Wall Street Journal poll conducted the same year surveyed 1200 people and found 720 supported same-sex marriage.a. Find both sample proportions and compare them.b. Test the hypothesis
California’s controversial “three-strikes law” requires judges to sentence anyone convicted of three felony offenses to life in prison. Supporters say that this decreases crime both because it is a strong deterrent and because career criminals are removed from the streets. Opponents argue
Patients with gout also have an increased risk of cardiovascular disease. A 2018 double- blind study by White et al. reported in The New England Journal of Medicine, patients with cardiovascular disease and gout were randomly assigned to receive one of two drugs: febuxostat or allopurinol. The
In 2015 a Gallup poll reported that 52% of Americans were satisfied with the quality of the environment. In 2018, a survey of 1024 Americans found that 461 were satisfied with the quality of the environment. Does this survey provide evidence that satisfaction with the quality of the environment
Dolly the Sheep, the world’s first mammal to be cloned, was introduced to the public in 1997. In a Pew Research poll taken soon after Dolly’s debut, 63% of Americans were opposed to the cloning of animals. In a Pew Research poll taken 20 years after Dolly, 60% of those surveyed were opposed to
A friend claims he can predict the suit of a card drawn from a standard deck of 52 cards. There are four suits and equal numbers of cards in each suit. The parameter, p, is the probability of success, and the null hypothesis is that the friend is just guessing.a. Which is the correct null
A friend claims he can predict how a six-sided die will land. The parameter, p, is the long run likelihood of success, and the null hypothesis is that the friend is guessing.a. Pick the correct null hypothesis.i. p = 1/6 ii. p > 1/6 iii. p
Judging on the basis of experience, a politician claims that 50% of voters in Pennsylvania have voted for an independent candidate in past elections. Suppose you surveyed 20 randomly selected people in Pennsylvania, and 12 of them reported having voted for an independent candidate. The null
The mother of a teenager has heard a claim that 25% of teenagers who drive and use a cell phone reported texting while driving. She thinks that this rate is too high and wants to test the hypothesis that fewer than 25% of these drivers have texted while driving. Her alternative hypothesis is that
A teacher giving a true/false test wants to make sure her students do better than they would if they were simply guessing, so she forms a hypothesis to test this. Her null hypothesis is that a student will get 50% of the questions on the exam correct. The alternative hypothesis is that the student
Suppose a friend says he can predict whether a coin flip will result in heads or tails. You test him, and he gets 10 right out of 20. Do you think he can predict the coin flip (or has a way of cheating)? Or could this just be something that occurs by chance? Explain without doing any calculations.
Suppose a friend says he can predict whether a coin flip will result in heads or tails. You test him, and he gets 20 right out of 20. Do you think he can predict the coin flip (or has a way of cheating)? Or could this just be something that is likely to occur by chance? Explain without performing
In the mid-1800s, Dr. Ignaz Semmelweiss decided to make doctors wash their hands with a strong disinfectant between patients at a clinic with a death rate of 9.9%. Semmelweiss wanted to test the hypothesis that the death rate would go down after the new handwashing procedure was used. What null and
Suppose you wanted to test the claim that the majority of U.S. voters are satisfied with the government response to the opioid crisis. State the null and alternative hypotheses you would use in both words and symbols.
A true/false test has 50 questions. Suppose a passing grade is 35 or more correct answers. Test the claim that a student knows more than half of the answers and is not just guessing. Assume the student gets 35 answers correct out of 50. Use a significance level of 0.05. Steps 1 and 2 of a
A multiple-choice test has 50 questions with four possible options for each question. For each question, only one of the four options is correct. A passing grade is 35 or more correct answers.a. What is the probability that a person will guess correctly on one multiple- choice question?b. Test the
The distribution of the scores on a certain exam is N(80, 5) which means that the exam scores are Normally distributed with a mean of 80 and a standard deviation of 5.a. Sketch or use technology to create the curve and label on the x-axis the position of the mean, the mean plus or minus one
The distribution of the scores on a certain exam is N(100, 10) which means that the exam scores are Normally distributed with a mean of 100 and a standard deviation of 10.a. Sketch or use technology to create the curve and label on the x-axis the position of the mean, the mean plus or minus one
According to home-water-works.org, the average shower in the United States lasts 8.2 minutes. Assume this is correct, and assume the standard deviation of 2 minutes.a. Do you expect the shape of the distribution of shower lengths to be Normal, right skewed, or left-skewed? Explain.b. Suppose that
According to a 2017 report by ComScore.com, the mean time spent on smartphones daily by the American adults is 2.85 hours. Assume this is correct and assume the standard deviation is 1.4 hours.a. Suppose 150 American adults are randomly surveyed and asked how long they spend on their smartphones
Drivers in Wyoming drive more miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Wyoming is 22,306 miles. Assume the standard deviation is 5500 miles. A random sample of 200 licensed drivers in Wyoming is selected and the mean number of miles
Drivers in Alaska drive fewer miles yearly than motorists in any other state. The annual number of miles driven per licensed driver in Alaska is 9134 miles. Assume the standard deviation is 3200 miles. A random sample of 100 licensed drivers in Alaska is selected and the mean number of miles driven
According to a 2018 Money magazine article, Maryland has one of the highest per capita incomes in the United States, with an average income of $75,847. Suppose the standard deviation is $32,000 and the distribution is right-skewed. A random sample of 100 Maryland residents is taken.a. Is the sample
According to a 2018 Money magazine article, the average income in Kansas is $53,906. Suppose the standard deviation is $3000 and the distribution of income is rightskewed. Repeated random samples of 400 Kansas residents are taken, and the sample mean of incomes is calculated for each sample.a. The
One histogram shows the distribution of costs for all used Toyota Sienna vans for sale within a 100 mile radius of San Leandro, CA, for a day in 2018. The other three graphs show distributions of means from random samples taken from this population based on samples of 2 vans, 5 vans, and 15 vans.
The undergraduate grade point average (GPA) for students accepted at a random sample of 10 medical schools in the United States was taken. The mean GPA for these accepted students was 3.75 with a standard error of 0.06. The distribution of undergraduate GPAs is Normal.a. Decide whether each of the

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Introductory Statistics Exploring The World Through Data 3rd Edition Robert Gould, Rebecca Wong, Colleen N. Ryan - Solutions

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