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intro stats

Stats Data And Models 4th Global Edition Richard D. De Veaux, Paul Velleman, David E. Bock - Solutions

Equal opportunity? A company is sued for job discrimination because only 11% of the newly hired candidates were minorities when 19% of all applicants were minorities.Is this strong evidence that the company’s hiring practices are discriminatory?a) Is this a one-tailed or a two-tailed test? Why?b)
Production Consider again the task of the quality control inspectors in Exercise 34.a) In this context, what is meant by the power of the test the inspectors conduct?b) They are currently testing 5 items each hour. Someone has proposed that they test 10 instead. What are the advantages and
Cars, again As in Exercise 33, state regulators are checking up on repair shops to see if they are certifying vehicles that do not meet pollution standards.a) In this context, what is meant by the power of the test the regulators are conducting?b) Will the power be greater if they test 20 or 40
Quality control Production managers on an assembly line must monitor the output to be sure that the level of defective products remains small. They periodically inspect a random sample of the items produced. If they find a significant increase in the proportion of items that must be rejected, they
Testing cars A clean air standard requires that vehicle exhaust emissions not exceed specified limits for various pollutants. Many states require that cars be tested annually to be sure they meet these standards. Suppose state regulators double-check a random sample of cars that a suspect repair
Alzheimer’s Testing for Alzheimer’s disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon et al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior
Homeowners 2013 In 2013, the U.S. Census Bureau reported that 65% of American families owned their homes—the lowest rate in 18 years. Census data reveal that the ownership rate in one small city is much lower.The city council is debating a plan to offer tax breaks to first-time home buyers in
More spam Consider again the points-based spam filter described in Exercise 28. When the points assigned to various components of an e-mail exceed the cutoff value you’ve set, the filter rejects its null hypothesis (that the message is real) and diverts that e-mail to a junk mailbox.a) In this
Second loan Exercise 27 describes the loan score method a bank uses to decide which applicants it will lend money. Only if the total points awarded for various aspects of an applicant’s financial condition fail to add up to a minimum cutoff score set by the bank will the loan be denied.a) In this
Spam Spam filters try to sort your e-mails, deciding which are real messages and which are unwanted. One method used is a point system. The filter reads each incoming e-mail and assigns points to the sender, the subject, key words in the message, and so on. The higher the point total, the more
Loans Before lending someone money, banks must decide whether they believe the applicant will repay the loan. One strategy used is a point system. Loan officers assess information about the applicant, totaling points they award for the person’s income level, credit history, current debt burden,
Fans A survey of 81 randomly selected people standing in line to enter a football game found that 73 of them were home team fans.a) Explain why we cannot use this information to construct a confidence interval for the proportion of all people at the game who are fans of the home team.*b) Construct
Dogs Canine hip dysplasia is a degenerative disease that causes pain in many dogs. Sometimes advanced warning signs appear in puppies as young as 6 months.A veterinarian checked 42 puppies whose owners brought them to a vaccination clinic, and she found 5 with early hip dysplasia. She considers
Hard times In June 2010, a random poll of 800 working men found that 9% had taken on a second job to help pay the bills. (www.careerbuilder.com)a) Estimate the true percentage of men that are taking on second jobs by constructing a 95% confidence interval.b) A pundit on a TV news show claimed that
Approval 2014 In March 2014, Barack Obama’s approval rating stood at 40% in Gallup’s daily tracking poll of 1500 randomly surveyed U.S. adults. (http://www.gallup.com/poll/113980/gallup-daily-obama-job-approval.aspx)a) Make a 95% confidence interval for his approval rating by all U.S. adults.b)
Is the Euro fair? Soon after the Euro was introduced as currency in Europe, it was widely reported that someone had spun a Euro coin 250 times and gotten heads 140 times. We wish to test a hypothesis about the fairness of spinning the coin.a) Estimate the true proportion of heads. Use a 95%
Groceries In January 2011, Yahoo surveyed 2400 U.S.men. 1224 of the men identified themselves as the primary grocery shopper in their household.a) Estimate the percentage of all American males who identify themselves as the primary grocery shopper.Use a 98% confidence interval. Check the conditions
Significant again? A new reading program may reduce the number of elementary school students who read below grade level. The company that developed this program supplied materials and teacher training for a large-scale test involving nearly 9300 children in several different school districts.
Significant? Public health officials believe that 90.6% of children have been vaccinated against measles. A random survey of medical records at many schools across the country found that, among more than 13,000 children, only 89.1% had been vaccinated. A statistician would reject the 90% hypothesis
Alpha, again Environmentalists concerned about the impact of high-frequency radio transmissions on birds found that there was no evidence of a higher mortality rate among hatchlings in nests near cell towers. They based this conclusion on a test using a = 0.05. Would they have made the same
Alpha A researcher developing scanners to search for hidden weapons at airports has concluded that a new device is significantly better than the current scanner.He made this decision based on a test using a = 0.05.Would he have made the same decision at a = 0.20?How about a = 0.001? Explain.
Another P-value Have harsher penalties and ad campaigns increased seat-belt use among drivers and passengers? Observations of commuter traffic failed to find evidence of a significant change compared with three years ago. Explain what the study’s P-value of 0.48 means in this context.
P-value A medical researcher tested a new treatment for poison ivy against the traditional ointment. He concluded that the new treatment is more effective. Explain what the P-value of 0.027 means in this context.
Which alternative? In each of the following situations, is the alternative hypothesis one-sided or two-sided?What are the hypotheses?a) A college dining service conducts a survey to see if students prefer plastic or metal cutlery.b) In recent years, 10% of college juniors have applied for study
One sided or two? In each of the following situations, is the alternative hypothesis one-sided or two-sided? What are the hypotheses?a) A business student conducts a taste test to see whether students prefer Diet Coke or Diet Pepsi.b) PepsiCo recently reformulated Diet Pepsi in an attempt to appeal
More errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made.a) A test of H0: m = 25 vs. HA: m 7 25 rejects the null hypothesis. Later it is discovered that m = 24.9.b) A test of H0: p = 0.8 vs. HA: p 6 0.8 fails to reject the null hypothesis.
Errors For each of the following situations, state whether a Type I, a Type II, or neither error has been made. Explain briefly.a) A bank wants to know if the enrollment on their website is above 30% based on a small sample of customers.They test H0: p = 0.3 vs. HA: p 7 0.3 and reject the null
More critical values For each of the following situations, find the critical value for z or t.a) H0: m = 106 vs. HA: m 106 at a = 0.05; n = 81.b) H0: p = 0.08 vs. HA: p 7 0.08 at a = 0.10.c) H0: p = 0.5 vs. HA: p 0.5 at a = 0.01.d) H0: p = 0.2 vs. HA: p 6 0.2 at a = 0.01; n = 400.e) H0: p = 0.1
Critical values For each of the following situations, find the critical value(s) for z or t.a) H0: p = 0.5 vs. HA: p 0.5 at a = 0.05.b) H0: p = 0.4 vs. HA: p 7 0.4 at a = 0.05.c) H0: m = 10 vs. HA: m 10 at a = 0.05; n = 36.d) H0: p = 0.5 vs. HA: p 7 0.5 at a = 0.01; n = 345.e) H0: m = 20 vs.
Alpha false and true Which of the following statements are true? If false, explain briefly.a) It is better to use an alpha level of 0.05 than an alpha level of 0.01.b) If we use an alpha level of 0.01, then a P-value of 0.001 is statistically significant.c) If we use an alpha level of 0.01, then we
Alpha true and false Which of the following statements are true? If false, explain briefly.a) Using an alpha level of 0.05, a P-value of 0.04 results in rejecting the null hypothesis.b) The alpha level depends on the sample size.c) With an alpha level of 0.01, a P-value of 0.10 results in rejecting
More hypotheses For each of the following, write out the alternative hypothesis, being sure to indicate whether it is one-sided or two-sided.a) Consumer Reports discovered that 20% of a certain computer model had warranty problems over the first three months. From a random sample, the manufacturer
Hypotheses For each of the following, write out the null and alternative hypotheses, being sure to state whether the alternative is one-sided or two-sided.a) A company reports that last year, 40% of their reports in accounting were on time. From a random sample this year, they want to know if that
More P-values Which of the following are true? If false, explain briefly.a) A very low P-value provides evidence against the null hypothesis.b) A high P-value is strong evidence in favor of the null hypothesis.c) A P-value above 0.10 shows that the null hypothesis is true.d) If the null hypothesis
P-values Which of the following are true? If false, explain briefly.a) A very high P-value is strong evidence that the null hypothesis is false.b) A very low P-value proves that the null hypothesis is false.c) A high P-value shows that the null hypothesis is true.d) A P-value below 0.05 is always
Hypotheses and parameters As in Exercise 1, for each of the following situations, define the parameter and write the null and alternative hypotheses in terms of parameter values.a) Seat-belt compliance in Massachusetts was 65% in 2008. The state wants to know if it has changed.b) Last year, a
Parameters and hypotheses For each of the following situations, define the parameter (proportion or mean)and write the null and alternative hypotheses in terms of parameter values. Example: We want to know if the proportion of up days in the stock market is 50%. Answer: Let p = the proportion of up
The study of Avandia published in the NEJM combined results from 47 different trials—a method called meta-analysis. The drug’s manufacturer, GlaxoSmithKline(GSK), issued a statement that pointed out, “Each study is designed differently and looks at unique questions: For example, individual
A published study found the risk of heart attack to be increased in patients taking the diabetes drug Avandia. The issue of the New England Journal of Medicine(NEJM ) in which that study appeared also included an editorial that said, in part,“A few events either way might have changed the
The baseline seven-year risk of heart attacks for diabetics is 20.2%. A NEJM study reported a 95% confidence interval equivalent to 20.8% to 40.0% for the risk among patients taking the diabetes drug Avandia.Question: What did this confidence interval suggest to the FDA about the safety of the drug?
Surgeons examined their results to compare two methods for a surgical procedure used to alleviate pain on the outside of the wrist. A new method was compared with the traditional “freehand” method for the procedure. Of 45 operations using the“freehand” method, three were unsuccessful, for a
Motor vehicle crashes are a leading cause of death for people between 4 and 33 years old. In the past 10 years motor vehicle accidents have claimed the lives of over 40,000 people a year in the United States. This means that, on average, motor vehicle crashes resulted in about 110 deaths each day,
The question of whether the diabetes drug Avandia increased the risk of heart attack was raised by a study in the New England Journal of Medicine. This study estimated the seven-year risk of heart attack to be 28.9% and reported a P-value of 0.03 for a test of whether this risk was higher than the
A New England Journal of Medicine paper reported that the seven-year risk of heart attack in diabetes patients taking the drug Avandia was increased from the baseline of 20.2% to an estimated risk of 28.9% and said the P-value was 0.03.Question: How should the P-value be interpreted in this context?
The diabetes drug Avandia® was approved to treat Type 2 diabetes in 1999. But an article in the New England Journal of Medicine (NEJM)1 raised concerns that the drug might carry an increased risk of heart attack. This study combined results from a number of other separate studies to obtain an
Wind power Should you generate electricity with your own personal wind turbine? That depends on whether you have enough wind on your site. To produce enough energy, your site should have an annual average wind speed above 8 miles per hour, according to the Wind Energy Association. One candidate
Golf drives III 2013 In Chapter 3 we looked at distance that 155 professional golfers drove the ball (in yds) during a week in 2013. Here is a histogram of those drives (espn.go.com/golf/statistics/_/year/2013/type/expanded). Assuming this is a representative sample of all professional golfers,a)
Braking A tire manufacturer is considering a newly designed tread pattern for its all-weather tires. Tests have indicated that these tires will provide better gas mileage and longer tread life. The last remaining test is for braking effectiveness. The company hopes the tire will allow a car
Maze Psychology experiments sometimes involve testing the ability of rats to navigate mazes. The mazes are classified according to difficulty, as measured by the mean length of time it takes rats to find the food at the end. One researcher needs a maze that will take rats an average of about one
Yogurt Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:130 160 150 120 120 110 170 160 110 130 9a) Check the assumptions and conditions for inference.b) Create a 95% confidence interval for the average calorie content of vanilla yogurt.c) A diet
Chips Ahoy! In 1998, as an advertising campaign, the Nabisco Company announced a “1000 Chips Challenge,”claiming that every 18-ounce bag of their Chips Ahoy! cookies contained at least 1000 chocolate chips. Dedicated Statistics students at the Air Force Academy (no kidding) purchased some
Ski wax Bjork Larsen was trying to decide whether to use a new racing wax for cross-country skis. He decided that the wax would be worth the price if he could average less than 55 seconds on a course he knew well, so he planned to test the wax by racing on the course 8 times. His 8 race times were
Popcorn Yvon Hopps ran an experiment to test optimum power and time settings for microwave popcorn. His goal was to find a combination of power and time that would deliver high-quality popcorn with less than 10% of the kernels left unpopped, on average.After experimenting with several bags, he
Doritos Some students checked 6 bags of Doritos marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights (in grams): 29.2, 28.5, 28.7, 28.9, 29.1, 29.5.a) Do these data satisfy the assumptions for inference?Explain.b) Find the mean and
Ruffles Students investigating the packaging of potato chips purchased 6 bags of Lay’s Ruffles marked with a net weight of 28.3 grams. They carefully weighed the contents of each bag, recording the following weights(in grams): 29.3, 28.2, 29.1, 28.7, 28.9, 28.5.a) Do these data satisfy the
Saving gas Congress regulates corporate fuel economy and sets an annual gas mileage for cars.A company with a large fleet of cars hopes to meet the goal of 32.6 mpg or better for their fleet of cars.To see if the goal is being met, they check the gasoline usage for 34 company trips chosen at
Marriage In 1960, census results indicated that the age at which American men first married had a mean of 23.3 years.It is widely suspected that young people today are waiting longer to get married. We want to find out if the mean age of first marriage has increased during the past 40 years.a)
Computer lab fees The technology committee has stated that the average time spent by students per lab visit has increased, and the increase supports the need for increased lab fees. To substantiate this claim, the committee randomly samples 12 student lab visits and notes the amount of time spent
Fuel economy 2014 revisited In Chapter 6, we examined the average fuel economy of several 2014 model vehicles.a) Find and interpret a 95% confidence interval for the gas mileage of 2014 vehicles.b) Do you think that this confidence interval captures the mean gas mileage for all 2014 vehicles?
Golf balls The United States Golf Association (USGA)sets performance standards for golf balls. For example, the initial velocity of the ball may not exceed 250 feet per second when measured by an apparatus approved by the USGA. Suppose a manufacturer introduces a new kind of ball and provides a
Pizza A researcher tests whether the mean cholesterol level among those who eat frozen pizza exceeds the value considered to indicate a health risk. She gets a P-value of 0.09. Explain in this context what the “9%”represents.
Hot dogs A nutrition lab tested 40 hot dogs to see if their mean sodium content was less than the 325-mg upper limit set by regulations for “reduced sodium” franks. The lab failed to reject the hypothesis that the hot dogs did not meet this requirement, with a P-value of 0.142. A 90%confidence
Farmed salmon, second look This chapter’s For Examples looked at mirex contamination in farmed salmon. We first found a 95% confidence interval for the mean concentration to be 0.0834 to 0.0992 parts per million. Later we rejected the null hypothesis that the mean did not exceed the EPA’s
Flight on time 2013 revisited Will your flight get you to your destination on time? The U.S. Bureau of Transportation Statistics reported the percentage of flights that were delayed each month from 1994 through October of 2013. Here’s a histogram, along with some summary statistics:We can
Flight on time 2013 What are the chances your flight will leave on time? The U.S. Bureau of Transportation Statistics of the Department of Transportation publishes information about airline performance. We saw the data in a Just Checking exercise in Chapter 4. Here are a histogram and summary
Better light After his first attempt to determine the speed of light (described in Exercise 27), Michelson conducted an“improved” experiment. In 1897, he reported results of 100 trials with a mean of 852.4 and a standard deviation of 79.0.a) What is the standard error of the mean for these
Speed of light In 1882, Michelson measured the speed of light (usually denoted c as in Einstein’s famous equation E = mc2). His values are in km/sec and have 299,000 subtracted from them. He reported the results of 23 trials with a mean of 756.22 and a standard deviation of 107.12.a) Find a 95%
Parking II Suppose that, for budget planning purposes, the city in Exercise 24 needs a better estimate of the mean daily income from parking fees.a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. How would this interval be
Normal temperatures, part II Consider again the statistics about human body temperature in Exercise 23.a) Would a 90% confidence interval be wider or narrower than the 98% confidence interval you calculated before? Explain. (Don’t compute the new interval.)b) What are the advantages and
Parking Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $129, with a standard deviation of $16.a)
Normal temperature The researcher described in Exercise 19 also measured the body temperatures of that randomly selected group of adults. Here are summaries of the data he collected. We wish to estimate the average(or “normal”) temperature among the adult population.a) Check the conditions for
Credit card charges A credit card company takes a random sample of 100 cardholders to see how much they charged on their card last month. Here’s a histogram.A computer program found that the resulting 95%confidence interval for the mean amount spent in March 2011 is ( - +28,366.84, +90,691.49).
CEO compensation A sample of 20 CEOs from the Forbes 500 shows total annual compensations ranging from a minimum of $0.1 to $62.24 million. The average for these 20 CEOs is $7.946 million. Here’s a histogram:Based on these data, a computer program found that a 95% confidence interval for the mean
Crawling Data collected by child development scientists produced this confidence interval for the average age(in weeks) at which babies begin to crawl:a) Explain carefully what the software output means.b) What is the margin of error for this interval?c) If the researcher had calculated a 90%
Pulse rates A medical researcher measured the pulse rates (beats per minute) of a sample of randomly selected adults and found the following Student’s t-based confidence interval:a) Explain carefully what the software output means.b) What’s the margin of error for this interval?c) If the
Snow Based on meteorological data for the past century, a local TV weather forecaster estimates that the region’s average winter snowfall is 23", with a margin of error of {2 inches. Assuming he used a 95% confidence interval, how should viewers interpret this news?Comment on each of these
Meal plan After surveying students at Dartmouth College, a campus organization calculated that a 95%confidence interval for the mean cost of food for one term (of three in the Dartmouth trimester calendar) is($1372, $1562). Now the organization is trying to write its report and is considering the
Teachers Software analysis of the salaries of a random sample of 288 Nevada teachers produced the confidence interval shown below. Which conclusion is correct?What’s wrong with the others?a) If we took many random samples of 288 Nevada teachers, about 9 out of 10 of them would produce this
Cattle Livestock are given a special feed supplement to see if it will promote weight gain. Researchers report that the 77 cows studied gained an average of 56 pounds, and that a 95% confidence interval for the mean weight gain this supplement produces has a margin of error of {11 pounds. Some
A good book An English professor is attempting to estimate the mean number of novels that the student body reads during their time in college. He is conducting an exit survey with seniors. He hopes to have a margin of error of 4 books with 95% confidence. From reading previous studies, he expects a
Jelly A consumer advocate wants to collect a sample of jelly jars and measure the actual weight of the product in the container. He needs to collect enough data to construct a confidence interval with a margin of error of no more than 2 grams with 95% confidence. The standard deviation of these
Home prices II Suppose the standard deviation of home price losses had been $3000, as in Exercise 8? What would your conclusion be then?
Home prices The last census of the entire community from which the sample in Exercise 7 was taken was 2010 when the mean loss was $10,200. From the sample in Exercise 7, use a t-test to test whether the mean loss has decreased.
t-models, last time Using the t tables, software, or a calculator, estimatea) the P-value for t … 2.19 with 41 degrees of freedom.b) the P-value for • t • 7 2.33 with 12 degrees of freedom.
t-models, again Using the t tables, software, or a calculator, estimatea) the P-value for t Ú 1.69 with 6 degrees of freedom.b) the P-value for • t • 7 1.89 with 24 degrees of freedom.
Home sales again In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value.a) Suppose the standard deviation of the losses had been $3000 instead of $1500. What would the larger standard deviation do to the width of the confidence interval (assuming
Home sales The housing market has recovered slowly from the economic crisis of 2008. Recently, in one large community, realtors randomly sampled 36 bids from potential buyers to estimate the average loss in home value. The sample showed the average loss from the peak in 2008 was $9,560 with a
t-models, part IV Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
t-models, part III Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
t-models, part II Using the t tables, software, or a calculator, estimatea) the critical value of t for a 99% confidence interval with df = 2.b) the critical value of t for a 90% confidence interval with df = 111.
t-models, part I Using the t tables, software, or a calculator, estimatea) the critical value of t for a 99% confidence interval with df = 12.b) the critical value of t for a 98% confidence interval with df = 92.
LSAT The LSAT (a test taken for law school admission)has a mean score of 151 with a standard deviation of 9 and a unimodal, symmetric distribution of scores. A test preparation organization teaches small classes of 9 students at a time. A larger organization teaches classes of 25 students at a
Salmon A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 37 pounds with a standard deviation of 4 pounds. The company ships them to restaurants in boxes of 4 salmon, to grocery stores in cartons of 16 salmon, and to discount outlet stores in
Let’s build a 90% confidence interval for the mean amount that college students sleep in a night.Question: What can we say about the mean amount of sleep that college students get?
Based on weighing thousands of animals, the American Angus Association reports that mature Angus cows have a mean weight of 1309 pounds with a standard deviation of 157 pounds. This result was based on a very large sample of animals from many herds over a period of 15 years, so let’s assume that
AP Stats The College Board reported that 57.9% of all students who took the 2013 AP Statistics exam earned scores of 3 or higher. One teacher wondered if the performance of her school was better. She believed that year’s students to be typical of those who will take AP Stats at that school and
John Wayne Like a lot of other Americans, John Wayne died of cancer. But is there more to this story? In 1955, Wayne was in Utah shooting the film The Conqueror.Across the state line, in Nevada, the United States military was testing atomic bombs. Radioactive fallout from those tests drifted across
TV ads A start-up company is about to market a new computer printer. It decides to gamble by running commercials during the Super Bowl. The company hopes that name recognition will be worth the high cost of the ads.The goal of the company is that over 36% of the public recognize its brand name and
Lost luggage An airline’s public relations department says that the airline rarely loses passengers’ luggage. It further claims that on those occasions when luggage is lost, 89% is recovered and delivered to its owner within 24 hours. A consumer group that surveyed a large number of air
Acid rain A study of the effects of acid rain on trees in the Hopkins Forest shows that 25 of 100 trees sampled exhibited some sort of damage from acid rain. This rate seemed to be higher than the 15% quoted in a recent Environmetrics article on the average proportion of damaged trees in the

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