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

A friend of yours claims that when he tosses a coin he can control the outcome. You are skeptical and want him to prove it. He tosses the coin, and you call heads; it's tails. You try again and lose again. a) Do two losses in a row convince you that he really can control the toss? Explain. b) You
Someone hands you a box of a dozen chocolate-covered candies, telling you that half are vanilla creams and the other half peanut butter. You pick candies at random and discover the first three you eat are all vanilla. a) If there really were 6 vanilla and 6 peanut butter candies in the box, what is
Many people have trouble setting up all the features of their smartphones, so a company has developed what it hopes will be easier instructions. The goal is to have at least 96% of customers succeed. The company tests the new system on 200 people, of whom 188 were successful. Is this strong
A friend of yours claims to be psychic. You are skeptical. To test this you take a stack of 100 playing cards and have your friend try to identify the suit (hearts, diamonds, clubs, or spades), without looking, of course! a) State the null hypothesis for your experiment. b) State the alternative
In 2008, the Centers for Disease Control and Prevention reported that 34% of adults in the United States are obese. A county health service planning a new awareness campaign polls a random sample of 750 adults living there. In this sample, 228 people were found to be obese based on their answers to
In a rural area, only about 30% of the wells that are drilled find adequate water at a depth of 100 feet or less. A local man claims to be able to find water by "dowsing"—using a forked stick to indicate where the well should be drilled. You check with 80 of his customers and find that 27 have
In the 1980s, it was generally believed that congenital abnormalities affected about 5% of the nation's children. Some people believe that the increase in the number of chemicals in the environment has led to an increase in the incidence of abnormalities. A recent study examined 384 children and
The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 34% of students had not been absent from school even once during the previous month. In the 2000 survey,
The National Center for Education Statistics monitors many aspects of elementary and secondary education nationwide. Their 1996 numbers are often used as a baseline to assess changes. In 1996, 31% of students reported that their mothers had graduated from college. In 2000, responses from 8368
In Exercise 23 of Chapter 8, you learned that the Paralyzed Veterans of America is a philanthropic organization that relies on contributions. They send free mailing labels and greeting cards to potential donors on their list and ask for a voluntary contribution. To test a new campaign, the
In Exercise 24 of Chapter 8, you learned that First USA, a major credit card company, is planning a new offer for their current cardholders. First USA will give double airline miles on purchases for the next 6 months if the cardholder goes online and registers for this offer. To test the
According to the Law School Admission Council, in the fall of 2011, 71% of law school applicants were accepted to some law school. The training program LSATisfaction claims that 174 of the 240 students trained in 2011 were admitted to law school. You can safely consider these trainees to be
According to the Association of American Medical Colleges, only 42% of medical school applicants were admitted to a medical school in the fall of 2013. Upon hearing this, the trustees of Striving College expressed concern that only 34 of the 81 students in their class of 2013 who applied to medical
A company with a fleet of 150 cars found that the emissions systems of 7 out of the 22 they tested failed to meet pollution control guidelines. Is this strong evidence that more than 20% of the fleet might be out of compliance? Test an appropriate hypothesis and state your conclusion. Be sure the
A clinical trial compares the new drug described in Exercise 1 to aspirin. The group using the new drug had somewhat fewer heart attacks than those in the aspirin group. a) The P-value from the hypothesis test was 0.28. What do you conclude? b) What would you have concluded if the P-value had been
An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Sometimes in handling them the appliances get damaged. Even though the damage may be minor, the company must sell those machines at drastically reduced prices. The company goal is to keep the
A national vital statistics report indicated that about 3% of all births produced twins. Is the rate of twin births the same among very young mothers? Data from a large city hospital found that only 7 sets of twins were born to 469 teenage girls. Test an appropriate hypothesis and state your
During the 2013 season, the home team won 153 of the 245 regular-season National Football League games. Is this strong evidence of a home field advantage in professional football? Test an appropriate hypothesis and state your conclusion. Be sure the appropriate assumptions and conditions are
A magazine is considering the launch of an online edition. The magazine plans to go ahead only if it's convinced that more than 25% of current readers would subscribe. The magazine contacted a simple random sample of 500 current subscribers, and 137 of those surveyed expressed interest. What should
A garden center wants to store leftover packets of vegetable seeds for sale the following spring, but the center is concerned that the seeds may not germinate at the same rate a year later. The manager finds a packet of last year's green bean seeds and plants them as a test. Although the packet
A company is criticized because only 13 of 43 people in executive-level positions are women. The company explains that although this proportion is lower than it might wish, it's not a surprising value given that only 40% of all its employees are women. What do you think? Test an appropriate
Census data for a certain county show that 19% of the adult residents are Hispanic. Suppose 72 people are called for jury duty and only 9 of them are Hispanic. Does this apparent underrepresentation of Hispanics call into question the fairness of the jury selection system? Explain.
Some people are concerned that new tougher standards and high-stakes tests adopted in many states have driven up the high school dropout rate. The National Center for Education Statistics reported that the high school dropout rate for the year 2004 was 10.3%. One school district whose dropout rate
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 Northeast. Does
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, 90% is recovered and delivered to its owner within 24 hours. A consumer group that surveyed a large number of air travelers found that
The "psychic" friend from Exercise 2 correctly identified more than 25% of the cards. a) A hypothesis test gave a P-value of 0.014. What do you conclude? b) What would you conclude if the P-value had been 0.245?
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 40% of the public recognize its brand name and
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 the
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 was pleased
According to the 2010 Census, 16% of the people in the United States are of Hispanic or Latino origin. One county supervisor believes her county has a different proportion of Hispanic people than the nation as a whole. She looks at their most recent survey data, which was a random sample of 437
According to the 2010 Census, 11.4% of all housing units in the United States were vacant. A county supervisor wonders if her county is different from this. She randomly selects 850 housing units in her county and finds that 129 of the housing units are vacant. a) State the hypotheses. b) Name the
Occasionally, a report comes out that a drug that cures some disease turns out to have a nasty side effect. For example, some antidepressant drugs may cause suicidal thoughts in younger patients. A researcher wants to study such a drug and look for evidence that such side effects exist. a) If the
A specialty food company sells whole King Salmon to various customers. The mean weight of these salmon is 35 pounds with a standard deviation of 2 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 pallets
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. Exercise 7 The housing market has recovered slowly from the economic crisis of
Suppose the standard deviation of home price losses had been $3000, as in Exercise 8? What would your conclusion be then? Exercise 8 In the previous exercise, you found a 95% confidence interval to estimate the average loss in home value. Previous Exercise The housing market has recovered slowly
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 99% confidence. The standard deviation of these jars is
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 3 books with 95% confidence. From reading previous studies, he expects a large
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 students
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 confidence
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 following
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
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: With 95.00% Confidence, 70.887604 < µ(Pulse) < 74.497011 a) Explain carefully what the software output means. b) What's the margin
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 time.
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% confidence
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). Explain why the analysts
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.Summary TemperatureCount
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 $126, with a standard deviation of $15. a) What
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 disadvantages of the 98% confidence
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% confidence
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 data? b) Without
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 statistics for the
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 consider these data to be a
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 recommended safe level of 0.08 ppm
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 interval
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 0.07. Explain in this context what the "7%" represents.
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?
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 using the computer.
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) Write
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 2011 goal of 30.2 mpg or better for their fleet of cars. To see if the goal is being met, they check the gasoline usage for 50 company trips chosen at random,
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 assumptions
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
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 determined
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 56.3,
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 randomly selected
Consumer Reports tested 11 brands of vanilla yogurt and found these numbers of calories per serving:a) Check the assumptions and conditions for inference.b) Create a 95% confidence interval for the average calorie content of vanilla yogurt.c) A diet guide claims that you will get an average of 120
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 minute
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 traveling at 60
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. Assuming this is a representative sample of all professional golfers,a) Find a 95% confidence interval for the mean drive distance. b) Interpreting
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 site was
Describe how the shape, center, and spread of t-models change as the number of degrees of freedom increases.
Describe how the critical value of t for a 95% confidence interval changes as the number of degrees of freedom increases.
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 standard
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 the same level of
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%. a) A casino wants to know if their slot machine really
For each of the following situations, find the critical value for z or t. a) Ho: ( = 105 vs. HA: ( ≠ 105 at ( = 0.05; n = 61. b) Ho: p = 0.05 vs. HA: p > 0.05 at ( = 0.05. c) Ho: p = 0.6 vs. HA: p ≠ 0.6 at ( = 0.01 d) Ho: p = 0.5 vs. HA: p < 0.5 at ( = 0.01; n = 500. e) Ho: p = 0.2 vs. HA: p <
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 > 0.3 and reject the null
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: ( = 25 vs. HA: ( >25 rejects the null hypothesis. Later it is discovered that ix = 24.9. b) A test of HQ: p = 0.8 vs. HA: p
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 to teenagers.
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 abroad. The dean's
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 0.047 means in this context.
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 0.17 means in this context.
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 ( = 0.05. Would he have made the same decision at ( = 0.10? How about ( = 0.01? Explain.
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 ( = 0.05. Would they have made the same decision at ( =
Public health officials believe that 98% 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 97.4% had been vaccinated. A statistician would reject the 98% hypothesis with a P-value
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 survey found that 45% of the
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 8500 children in several different school districts. Statistical analysis of
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
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% confidence interval.
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, (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) Based on the
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 only 6%
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 this
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 a
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, and so
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 likely it
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 context,
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
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 context, what
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 order to encourage
Testing for Alzheimer's disease can be a long and expensive process, consisting of lengthy tests and medical diagnosis. A group of researchers (Solomon el al., 1998) devised a 7-minute test to serve as a quick screen for the disease for use in the general population of senior citizens. A patient

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