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intro stats

Intro Stats 4th International Edition Richard D. De Veaux, Paul F. Velleman, David Bock - Solutions

18. 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
17. 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 = 0.10?How about a = 0.01? Explain.
16. 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 0.17 means in this context.
15. 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 0.047 means in this context.
14. 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
13. 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
12. 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
11. 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
10. More critical values For each of the following situations, find the critical value for z or t.a) H0: m = 105 vs. HA: m 105 at a = 0.05; n = 61.b) H0: p = 0.05 vs. HA: p 7 0.05 at a = 0.05.c) H0: p = 0.6 vs. HA: p 0.6 at a = 0.01.d) H0: p = 0.5 vs. HA: p 6 0.5 at a = 0.01; n = 500.e) H0: p =
9. 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.
8. 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
7. 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
6. 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
5. 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
4. 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
3. 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
2. 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
1. 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
86. Rap Using the results of the experiment described in Exercise 85, does it matter whether one listens to rap music while studying, or is it better to study without music at all?a) Test an appropriate hypothesis and state your conclusion.b) If you concluded there is a difference, estimate the
85. Music and memory Is it a good idea to listen to music when studying for a big test? In a study conducted by some Statistics students, 62 people were randomly assigned to listen to rap music, music by Mozart, or no music while attempting to memorize objects pictured on a page. They were then
84. Golf again Given the test results on golf tees described in Exercise 83, is there evidence that balls hit off Stinger tees would travel farther? Again, assume that 6 balls were hit off each tee and that the data were suitable for inference.
83. Tees Does it matter what kind of tee a golfer places the ball on? The company that manufactures “Stinger”tees claims that the thinner shaft and smaller head will lessen resistance and drag, reducing spin and allowing the ball to travel farther. In August 2003, Golf Laboratories, Inc.,
82. Swimming heats In Exercise 81, we looked at the times in two different heats for the 400-m women’s run from the 2004 Olympics. Unlike track events, swimming heats are not determined at random. Instead, swimmers are seeded so that better swimmers are placed in later heats.Here are the times
81. Running heats In Olympic running events, preliminary heats are determined by random draw, so we should expect that the abilities of runners in the various heats to be about the same, on average. Here are the times(in seconds) for the 400-m women’s run in the 2004 Olympics in Athens for
80. Still swimming Here’s some additional information about the Ontario crossing times presented in Exercise 79.It is generally thought to be harder to swim across the lake from north to south. Indeed, this has been done only 5 times. Every one of those crossings was by a woman. If we omit those
79. Crossing Ontario Between 1954 and 2003, swimmers have crossed Lake Ontario 43 times. Both women and men have made the crossing. Here are some plots (we’ve omitted a crossing by Vikki Keith, who swam a round trip—North to South to North—in 3390 minutes):Summary statistics are as
78. Thirsty? Researchers randomly assigned participants either a tall, thin “highball” glass or a short, wide“tumbler,” each of which held 355 ml. Participants were asked to pour a shot (1.5 oz = 44.3 ml) into their glass.Did the shape glass make a difference in how much liquid they
77. Hungry? Researchers investigated how the size of a bowl affects how much ice cream people tend to scoop when serving themselves.14 At an “ice cream social,”people were randomly given either a 17 oz or a 34 oz bowl (both large enough that they would not be filled to capacity). They were then
76. Ad campaign You are a consultant to the marketing department of a business preparing to launch an ad campaign for a new product. The company can afford to run ads during one TV show, and has decided not to sponsor a show with sexual content. You read the study described in Exercise 75, then use
75. Sex and violence The Journal of Applied Psychology reported on a study that examined whether the content of TV shows influenced the ability of viewers to recall brand names of items featured in the commercials. The researchers randomly assigned volunteers to watch one of three programs, each
74. Summer school Having done poorly on their math final exams in June, six students repeat the course in summer school, then take another exam in August. If we consider these students representative of all students who might attend this summer school in other years, explain why you can’t use the
73. Job satisfaction A company institutes an exercise break for its workers to see if this will improve job satisfaction, as measured by a questionnaire that assesses workers’satisfaction. Scores for 10 randomly selected workers before and after implementation of the exercise program are shown.
72. Hard water In an investigation of environmental causes of disease, data were collected on the annual mortality rate (deaths per 100,000) for males in 61 large towns in England and Wales. In addition, the water hardness was recorded as the calcium concentration (parts per million, ppm) in the
71. Baseball American League baseball teams play their games with the designated hitter rule, meaning that pitchers do not bat. The league believes that replacing the pitcher, traditionally a weak hitter, with another player in the batting order produces more runs and generates more interest among
70. Memory Does ginkgo biloba enhance memory? In an experiment to find out, subjects were assigned randomly to take ginkgo biloba supplements or a placebo. Their memory was tested to see whether it improved. Here are boxplots comparing the two groups and in the next column is some computer output
69. Hurricanes The data below show the number of hurricanes(category 3 or higher) recorded annually before and after 1970. Create an appropriate visual display, and determine whether these data are appropriate for testing whether there has been a change in the frequency of hurricanes. 1944-1969 3,
68. Streams Researchers collected samples of water from streams in the Adirondack Mountains to investigate the effects of acid rain. They measured the pH (acidity) of the water and classified the streams with respect to the kind of substrate (type of rock over which they flow).A lower pH means the
67. Reading An educator believes that new reading activities for elementary school children will improve reading comprehension scores. She randomly assigns third graders to an eight-week program in which some will use these activities and others will experience traditional teaching methods. At the
66. Egyptians Some archaeologists theorize that ancient Egyptians interbred with several different immigrant populations over thousands of years. To see if there is any indication of changes in body structure that might have resulted, they measured 30 skulls of male Egyptians dated from 4000 b.c.e.
65. Cereal The data below show the sugar content (as a percentage of weight) of several national brands of children’s and adults’ cereals. Create and interpret a 95%confidence interval for the difference in mean sugar content.Be sure to check the necessary assumptions and
64. New construction The sample of 100 house sales we looked at in Exercise 63 also listed whether the home was new construction or not. Find and interpret a 95% confidence interval for how much more an agent can expect to sell a new home for. (From technology, df = 197.8.) Here are the summaries
63. View of the water How much extra is having a waterfront property worth? A student took a random sample of 170 recently sold properties in Upstate New York to examine the question. Here are her summaries and boxplots of the two groups of prices:Construct and interpret a 95% confidence interval
62. Pulse rates A researcher wanted to see whether there is a significant difference in resting pulse rates for men and women. The data she collected are displayed in the boxplots and summarized in the next column.a) What do the boxplots suggest about differences between male and female pulse
61. Commuting A man who moves to a new city sees that there are two routes he could take to work. A neighbor who has lived there a long time tells him Route A will average 5 minutes faster than Route B. The man decides to experiment. Each day, he flips a coin to determine which way to go, driving
60. CPMP and word problems The study of the new CPMP Mathematics methodology described in Exercise 57 also tested students’ abilities to solve word problems.This table shows how the CPMP and traditional groups performed. (The df are shown in Exercise 59.) What do you conclude? Math Program n Mean
59. CPMP, again During the study described in Exercise 57, students in both CPMP and traditional classes took another Algebra test that did not allow them to use calculators. The table below shows the results. Are the mean scores of the two groups significantly different?Performance on Algebraic
58. Stereograms Stereograms appear to be composed entirely of random dots. However, they contain separate images that a viewer can “fuse” into a three-dimensional(3D) image by staring at the dots while defocusing the eyes. An experiment was performed to determine whether knowledge of the form
57. Learning math The Core Plus Mathematics Project(CPMP) is an innovative approach to teaching Mathematics that engages students in group investigations and mathematical modeling. After field tests in 36 high schools over a three-year period, researchers compared the performances of CPMP students
56. Third load of wash In Exercise 54, we saw a 98%confidence interval of (-40, -22) minutes for mTop - mFront, the difference in time it takes top-loading and front-loading washers to do a load of clothes.Explain why you think each of the following statements is true or false:a) 98% of top loaders
55. Hot dogs, last one In Exercise 53, we saw a 90%confidence interval of (-6.5, -1.4) grams for mMeat - mBeef, the difference in mean fat content for meat vs. all-beef hot dogs. Explain why you think each of the following statements is true or false:a) If I eat a meat hot dog instead of a beef
54. Second load of wash The Consumer Reports article described in Exercise 52 continued their investigation of washing machines. One of the variables the article reported was “cycle time,” the number of minutes it took each machine to wash a load of clothes. Among the machines rated good to
53. Hot dogs, second helping The Consumer Reports article described in Exercise 51 also listed the fat content (in grams) for samples of beef and meat hot dogs. The resulting 90% confidence interval for mMeat - mBeef is(-6.5, -1.4).a) The endpoints of this confidence interval are negative numbers.
52. Washers In the June 2007 issue, Consumer Reports also examined the relative merits of top-loading and frontloading washing machines, testing samples of several different brands of each type. Suppose the study tested the null hypothesis that top- and front-loading machines don’t differ in
51. Hot dogs In the July 2007 issue, Consumer Reports examined the calorie content of two kinds of hot dogs:meat (usually a mixture of pork, turkey, and chicken) and all beef. The researchers purchased samples of several different brands. The meat hot dogs averaged 111.7 calories, compared to 135.4
50. Fast food The global survey we learned about in Exercise 49 also asked respondents how they felt about the statement “I try to avoid eating fast foods.” The random sample of 800 included 411 people 35 years old or younger, and of those, 197 agreed (completely or somewhat) with the
49. Food preference GfK Roper Consulting gathers information on consumer preferences around the world to help companies monitor attitudes about health, food, and healthcare products. They asked people in many different cultures how they felt about the following statement:I have a strong preference
48. Carbs Recently, the Gallup Poll asked 1005 U.S. adults if they actively try to avoid carbohydrates in their diet.That number increased to 27% from 20% in a similar 2002 poll. Is this a statistically significant increase?Explain.
47. Sensitive men In the same article from Exercise 46, Time magazine, reporting on a survey of men’s attitudes, noted that “Young men are more comfortable than older men talking about their problems.” The survey reported that 80 of 129 surveyed 18- to 24-year-old men and 98 of 184 25- to
46. Stay-at-home dads A Time magazine article about a survey of men’s attitudes reported that 11 of 161 black respondents and 20 of 358 Latino respondents responded“Yes” to the question “Are you a stay-at-home dad?”How big is the difference in proportions in the two populations?a)
45. Convention bounce Political pundits talk about the “bounce” that a presidential candidate gets after his party’s convention. In the past 40 years, it has averaged about 6 percentage points. Just before the 2004 Democratic convention, Rasmussen Reports polled 1500 likely voters at random
44. Gender gap Candidates for political office realize that different levels of support among men and women may be a crucial factor in determining the outcome of an election. One candidate finds that 52% of 473 men polled say they will vote for him, but only 45% of the 522 women in the poll express
43. Pain Researchers comparing the effectiveness of two pain medications randomly selected a group of patients who had been complaining of a certain kind of joint pain. They randomly divided these people into two groups, then administered the pain killers. Of the 112 people in the group who
42. Mammograms redux In 2001, the conclusion of the study outlined in Exercise 41 was questioned. A new 9-year study was conducted in Sweden, comparing 21,088 women who had mammograms with 21,195 who did not. Of the women who underwent screening, 63 died of breast cancer, compared to 66 deaths
41. Mammograms It’s widely believed that regular mammogram screening may detect breast cancer early, resulting in fewer deaths from that disease. One study that investigated this issue over a period of 18 years was published during the 1970s. Among 30,565 women who had never had mammograms, 196
40. Politics and sex One month before the election, a poll of 630 randomly selected voters showed 54% planning to vote for a certain candidate. A week later, it became known that he had had an extramarital affair, and a new poll showed only 51% of 1010 voters supporting him.Do these results
39. Birthweight The Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York’s World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy
38. Depression A study published in the Archives of General Psychiatry examined the impact of depression on a patient’s ability to survive cardiac disease.Researchers identified 450 people with cardiac disease, evaluated them for depression, and followed the group for 4 years. Of the 361 patients
37. Teen smoking, part I A Vermont study published by the American Academy of Pediatrics examined parental influence on teenagers’ decisions to smoke. A group of students who had never smoked were questioned about their parents’ attitudes toward smoking. These students were questioned again two
36. Anorexia again In Exercise 34, you used a confidence interval to examine the effectiveness of Prozac in treating anorexia nervosa. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.)a) What hypotheses would you test?b) State a
35. Another ear infection In Exercise 33, you used a confidence interval to examine the effectiveness of a vaccine against ear infections in babies. Suppose that instead you had conducted a hypothesis test. (Answer these questions without actually doing the test.)a) What hypotheses would you
34. Anorexia The Journal of the American Medical Association reported on an experiment intended to see if the drug Prozac® could be used as a treatment for the eating disorder anorexia nervosa. The subjects, women being treated for anorexia, were randomly divided into two groups. Of the 49 who
33. Ear infections A new vaccine was recently tested to see if it could prevent the painful and recurrent ear infections that many infants suffer from. The Lancet, a medical journal, reported a study in which babies about a year old were randomly divided into two groups. One group received
32. Race and smoking 2010 Data collected in 2010 by the Behavioral Risk Factor Surveillance System revealed that in the state of New Jersey, 15.7% of whites and 15.9% of blacks were cigarette smokers. Suppose these proportions were based on samples of 2449 whites and 464 blacks.a) Create a 90%
31. Prostate cancer There has been debate among doctors over whether surgery can prolong life among men suffering from prostate cancer, a type of cancer that typically develops and spreads very slowly. Recently, The New England Journal of Medicine published results of some Scandinavian research.
30. Carpal tunnel The painful wrist condition called carpal tunnel syndrome can be treated with surgery or less invasive wrist splints. Recently, Time magazine reported on a study of 176 patients. Among the half that had surgery, 80% showed improvement after three months, but only 48% of those who
29. Pets Researchers at the National Cancer Institute released the results of a study that investigated the effect of weed-killing herbicides on house pets. They examined 827 dogs from homes where an herbicide was used on a regular basis, diagnosing malignant lymphoma in 473 of them. Of the 130
28. Graduation In October 2000, the U.S. Department of Commerce reported the results of a large-scale survey on high school graduation. Researchers contacted more than 25,000 Americans aged 24 years to see if they had finished high school; 84.9% of the 12,460 males and 88.1% of the 12,678 females
27. Arthritis The Centers for Disease Control and Prevention reported a survey of randomly selected Americans age 65 and older, which found that 411 of 1012 men and 535 of 1062 women suffered from some form of arthritis.a) Are the assumptions and conditions necessary for inference satisfied?
26. Buy it again? A consumer magazine plans to poll car owners to see if they are happy enough with their vehicles that they would purchase the same model again.They’ll randomly select 450 owners of American-made cars and 450 owners of Japanese models. Obviously, the actual opinions of the entire
25. Gender gap A presidential candidate fears he has a problem with women voters. His campaign staff plans to run a poll to assess the situation. They’ll randomly sample 300 men and 300 women, asking if they have a favorable impression of the candidate. Obviously, the staff can’t know this, but
24. Regulating access When a random sample of 935 parents were asked about rules in their homes, 77% said they had rules about the kinds of TV shows their children could watch. Among the 790 of those parents whose teenage children had Internet access, 85% had rules about the kinds of Internet sites
23. Revealing information Eight hundred eight-six randomly sampled teens were asked which of several personal items of information they thought it okay to share with someone they had just met. Forty-four percent said it was okay to share their e-mail addresses, but only 29%said they would give out
22. Science news At the end of 2010, the Pew Project for Excellence in Journalism investigated where people are getting their news. In the study, 34% of responders said they read news online as opposed to 31% who favored newspapers. What does it mean to say that the difference is not significant?
21. Online social networking In April 2011, the Pew Internet and American Life Project surveyed 799 teenagers aged 12 to 17. Among the study’s findings, 93% of teen social media users have a Facebook account compared to only 24% who have a MySpace account. What does it mean to say that the
20. Athletes, final inning Looking back at Exercise 12, instead of comparing the ages of players in Major League Baseball to players in the National Football League, what if they had compared the ages in Major League Baseball to a Little League composed of third graders? Would the pooled t-test be
19. Cost of shopping, last look Looking back at Exercise 11, instead of comparing two very similar stores, suppose the researchers had compared purchases at two car dealerships: one that specializes in new Italian sports cars and another that carries used domestic vehicles. Would the pooled t-test
18. Athlete ages, one more time Repeat the test you did in Exercise 16, but assume that the variances of ages is the same in the two leagues. Did your conclusion change?Why do you think that is?
17. Cost of shopping, once more Repeat the test you did in Exercise 15, but assume that the variances of purchase amounts is the same at Target and Walmart. Did your conclusion change? Why do you think that is?
16. Athlete ages, three The researchers in Exercise 12 decide to test the hypothesis that the means are equal. The degrees of freedom formula gives 51.83 df. Test the null hypothesis at a = 0.05
15. Cost of shopping, three The researchers in Exercise 11 decide to test the hypothesis that the means are equal.The degrees of freedom formula gives 162.75 df. Test the null hypothesis at a = 0.05.
14. Athlete ages, again Using the summary statistics provided in Exercise 12, the sports reporter calculated the following 95% confidence interval for the mean difference between major league baseball players and professional football players. The 95% interval for mMLB - mNFL was (-0.41, 3.09).
13. Cost of shopping, again Using the summary statistics provided in Exercise 11, researchers calculated a 95%confidence interval for the mean difference between Walmart and Target purchase amounts. The interval was (- +14.15, - +1.85). Explain in context what this interval means.
12. Athlete ages A sports reporter suggests that professional baseball players must, on average, be older than professional football players, since football is a contact sport and players are more susceptible to concussions and serious injuries (www.sports.yahoo.com). One player was selected at
11. Cost of shopping Do consumers spend more on a trip to Walmart or Target? Suppose researchers interested in this question collected a systematic sample from 85 Walmart customers and 80 Target customers by asking customers for their purchase amount as they left the stores. The data collected is
10. Non-profits, last one The researchers from Exercise 2 want to test if the proportions of satisfied employees are the same at for-profit companies as at not-for-profit companies.a) What is the difference in the proportions of the two types of companies?b) What is the pooled proportion of
9. Canada, la fin The researchers from Exercise 1 want to test if the proportions of foreign born are the same in the United States as in Canada.a) What is the difference in the proportions of foreign born residents from both countries?b) What is the pooled proportion of foreign born in both
8. Non-profits, again For the interval given in Exercise 6, explain what “95% confidence” means.
7. Canada, encore For the interval given in Exercise 5, explain what “95% confidence” means.
6. Non-profits, part 3 The researchers from Exercise 2 created a 95% two-proportion confidence interval for the difference in those who are “highly satisfied” when comparing people who work at non-profits to people who work at for-profit companies. Interpret the interval with a sentence in
5. Canada, trois The information in Exercise 1 was used to create a 95% two-proportion confidence interval for the difference between Canadians and Americans who were born in foreign countries. Interpret this interval with a sentence in context.95% confidence interval for pCanadians - pAmericans is

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