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statistics principles and methods
Statistics The Exploration And Analysis Of Data 6th Edition John M Scheb, Jay Devore, Roxy Peck - Solutions
=+c. Explain why the confidence intervals of Parts (a) and
=+b. Construct a 95% confidence interval for the proportion of those who consider themselves to be baseball fans that think the designated hitter rule should be expanded to both leagues or eliminated.
=+a. Construct a 95% confidence interval for the proportion of U.S. adults that consider themselves to be baseball fans.
=+9.20 In an AP-AOL sports poll (Associated Press, December 18, 2005), 394 of 1000 randomly selected U.S. adults indicated that they considered themselves to be baseball fans. Of the 394 baseball fans, 272 stated that they thought the designated hitter rule should either be expanded to both
=+b. What are two reasons why a 90% confidence interval for the proportion of U.S. businesses that have fired workers for misuse of email would be narrower than the 95%confidence interval computed in Part (a).
=+a. Construct and interpret a 95% confidence interval for the proportion of U.S. businesses that have fired workers for misuse of the Internet.
=+9.19 The report “2005 Electronic Monitoring & Surveillance Survey: Many Companies Monitoring, Recording, Videotaping—and Firing—Employees” (American Management Association, 2005) summarized the results of a survey of 526 U.S. businesses. The report stated that 137 of the 526 businesses
=+b. Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the least favorite subject.
=+a. Construct a 95% confidence interval for the proportion of U.S. adults for whom math was the favorite subject in school.
=+9.18 In a survey of 1000 randomly selected adults in the United States, participants were asked what their most favorite and what their least favorite subject was when they were in school (Associated Press, August 17, 2005). In what might seem like a contradiction, math was chosen more often
=+b. Would a 99% confidence interval be wider or narrower than the 95% confidence interval from Part (a)?
=+a. Assuming that it is reasonable to regard this sample of 500 potential jurors as representative of potential jurors in the United States, use the given information to construct and interpret a 95% confidence interval for the true proportion of potential jurors who regularly watch at least one
=+9.17 ▼ The article “CSI Effect Has Juries Wanting More Evidence” (USA Today, August 5, 2004) examines how the popularity of crime-scene investigation television shows is influencing jurors’ expectations of what evidence should be produced at a trial. In a survey of 500 potential jurors,
=+c. Explain why the two 90% confidence intervals from Parts (a) and (b) are not the same width.
=+b. Construct a 90% confidence interval for the proportion of college seniors who carry a credit card balance from month to month.
=+a. Construct a 90% confidence interval for the proportion of college freshmen who carry a credit card balance from month to month.
=+9.16 The article “Students Increasingly Turn to Credit Cards” (San Luis Obispo Tribune, July 21, 2006) reported that 37% of college freshmen and 48% of college seniors carry a credit card balance from month to month. Suppose that the reported percentages were based on random samples of 1000
=+b. Do you think it is reasonable to generalize this estimate to other months of the year? Explain.
=+a. Construct and interpret a 99% confidence interval for the proportion of Americans who made plans in May 2005 based on an incorrect weather report.
=+9.15 According to an AP-Ipsos poll (June 15, 2005), 42%of 1001 randomly selected adult Americans made plans in May 2005 based on a weather report that turned out to be wrong.
=+9.14 Discuss how each of the following factors affects the width of the confidence interval for p:a. The confidence levelb. The sample sizec. The value of p
=+9.13 The use of the interval requires a large sample. For each of the following combinations of n and p, indicate whether the given interval would be appropriate.a. n 5 50 and p 5 .30b. n 5 50 and p 5 .05c. n 5 15 and p 5 .45d. n 5 100 and p 5 .01e. n 5 100 and p 5 .70f. n 5 40 and p 5 .25 g. n
=+9.12 The formula used to compute a large-sample confidence interval for p is What is the appropriate z critical value for each of the following confidence levels?a. 95%d. 80%b. 90%e. 85%c. 99%p 6 1z critical value 2B p11 2 p 2 n
=+9.11 ▼would result in a wider large-sample confidence interval for p:a. 90% confidence level or 95% confidence levelb. n 5 100 or n 5 400
=+d. Give a point estimate of the population median usage based on the given sample. Which statistic did you use?
=+c. Use the given data to estimate p, the proportion of all houses that used at least 100 therms.
=+b. Suppose that 10,000 houses in this area use natural gas for heating. Let t denote the total amount of gas used by all of these houses during January. Estimate t using the given data. What statistic did you use in computing your estimate?
=+103 156 118 89 125 147 122 109 138 99a. Let mJ denote the average gas usage during January by all houses in this area. Compute a point estimate of mJ.
=+9.10 ● A random sample of 10 houses in a particular area, each of which is heated with natural gas, is selected, and the amount of gas (in therms) used during the month of January is determined for each house. The resulting observations are as follows:
=+d. Suppose that the diameter distribution is normal. Then the 90th percentile of the diameter distribution is m 1 1.28s (so 90% of all trees have diameters less than this value). Compute a point estimate for this percentile. (Hint:First compute an estimate of m in this case; then use it along
=+c. Suppose that the population distribution of diameter is symmetric but with heavier tails than the normal distribution. Give a point estimate of the population mean diameter based on a statistic that gives some protection against the presence of outliers in the sample. What statistic did you
=+b. Making no assumptions about the shape of the population distribution of diameters, give a point estimate for the population median diameter. What statistic did you use to obtain the estimate?
=+a. Compute a point estimate of s, the population standard deviation of main stem diameter. What statistic did you use to obtain your estimate?
=+9.9 ● A random sample of n 5 12 four-year-old red pine trees was selected, and the diameter (in inches) of each tree’s main stem was measured. The resulting observations are as follows:11.3 10.7 12.4 15.2 10.1 12.1 16.2 10.5 11.4 11.0 10.7 12.0
=+b. Making no assumptions about the shape of the population distribution, estimate the proportion of all such cyclists whose gross efficiency is at most 20.
=+a. Assuming that the distribution of gross energy in the population of all endurance cyclists is normal, give a point estimate of m, the population mean gross efficiency.
=+9.8 ● The following data on gross efficiency (ratio of work accomplished per minute to calorie expenditure per minute) for trained endurance cyclists were given in the article “Cycling Efficiency Is Related to the Percentage of Type I Muscle Fibers” (Medicine and Science in Sports and
=+c. Use the given data to produce an estimate of s, the standard deviation of salt content. Is the statistic you used to produce your estimate unbiased?
=+b. Use the given data to produce a point estimate of s 2, the variance of salt content for frankfurters.
=+9.7 ● The article “Sensory and Mechanical Assessment of the Quality of Frankfurters” (Journal of Texture Studies[1990]: 395–409) reported the following salt content (percentage by weight) for 10 frankfurters:2.26 2.11 1.64 1.17 1.64 2.36 1.70 2.10 2.19 2.40a. Use the given data to
=+6 months after treatment (this figure is consistent with information given in the article). Estimate the percentage of all smokers who, when given this treatment, would refrain from smoking for at least 6 months.
=+9.6 A study reported in Newsweek (December 23, 1991)involved a sample of 935 smokers. Each individual received a nicotine patch, which delivers nicotine to the bloodstream but at a much slower rate than cigarettes do. Dosage was decreased to 0 over a 12-week period.Suppose that 245 of the
=+9.5 Each person in a random sample of 20 students at a particular university was asked whether he or she is registered to vote. The responses (R 5 registered, N 5 not registered) are given here:R R N R N N R R R N R R R R R N R R R N Use these data to estimate p, the true proportion of all
=+c. Use the given information to produce estimates of the standard deviations of calorie intake for days when no fast food is consumed and for days when fast food is consumed.
=+b. Use the given information to estimate the mean calorie intake for children in the United States on a day when fast food is consumed.
=+a. Use the given information to estimate the mean calorie intake for children in the United States on a day when no fast food is consumed.
=+No Fast Food 2331 1918 1009 1730 1469 2053 2143 1981 1852 1777 1765 1827 1648 1506 2669 Fast Food 2523 1758 934 2328 2434 2267 2526 1195 890 1511 875 2207 1811 1250 2117
=+9.4 ● Data consistent with summary quantities in the article referenced in Exercise 9.3 on total calorie consumption on a particular day are given for a sample of children who did not eat fast food on that day and for a sample of children who did eat fast food on that day. Assume that it is
=+9.3 Consumption of fast food is a topic of interest to researchers in the field of nutrition. The article “Effects of Fast-Food Consumption on Energy Intake and Diet Quality Among Children” (Pediatrics [2004]: 112–118) reported that 1720 of those in a random sample of 6212 U.S. children
=+9.2 Why is an unbiased statistic generally preferred over a biased statistic for estimating a population characteristic? Does unbiasedness alone guarantee that the estimate will cum unbi ing a
=+person innocent—not rejecting the null hypothesis of innocence when it is in fact false. If the developer of the lie detector is correct in his statements, what is the probability of a Type I error, a? What can you say about the probability of a Type II error, b?
=+In this situation, a Type I error is finding an innocent person guilty—rejecting the null hypothesis of innocence when it is in fact true. A Type II error is finding a guilty
=+basis of a decision between two rival hypotheses: accused is innocent versus accused is guilty. Although these are not “statistical hypotheses” (statements about a population characteristic), the possible decision errors are analogous to Type I and Type II errors.
=+10.95 A type of lie detector that measures brain waves was developed by a professor of neurobiology at Northwestern University (Associated Press, July 7, 1988). He said, “It would probably not falsely accuse any innocent people and it would probably pick up 70% to 90% of guilty people.”
=+false. Again, use Appendix Table 1 to simulate selecting a sample, and carry out the test. If you repeated this a total of 100 times, would you expect H0 to be rejected more frequently than when H0 is true?
=+c. Now suppose that p 5 .6, which implies that H0 is
=+b. If you repeated Part (a) a total of 100 times (a simulation consisting of 100 replications), how many times would you expect H0 to be rejected?
=+a. Suppose that H0 is in fact true. Use Appendix Table 1(our table of random numbers) to simulate selecting a sample, and use the resulting data to carry out the test.
=+10.94 Let p denote the proportion of voters in a certain state who favor a particular proposed constitutional amendment. Consider testing H0: p 5 .5 versus Ha: p . .5 at significance level .05 based on a sample of size n 5 50.
=+10.93 A hot tub manufacturer advertises that with its heating equipment, a temperature of 1008F can be achieved in at most 15 min. A random sample of 25 tubs is selected, and the time necessary to achieve a 1008F temperature is determined for each tub. The sample average time and sample standard
=+$75.00. The price was recently increased to $1.00 per can.A random sample of n 5 20 days after the price increase yielded a sample average daily revenue and sample standard deviation of $70.00 and $4.20, respectively. Does this information suggest that the true average daily revenue has
=+10.92 A student organization uses the proceeds from a particular soft-drink dispensing machine to finance its activities. The price per can had been $0.75 for a long time, and the average daily revenue during that period had been
=+Assuming that fuel efficiency is normally distributed under these circumstances, do the data contradict the claim that true average fuel efficiency is (at least) 30 mpg?
=+10.91 ● An automobile manufacturer who wishes to advertise that one of its models achieves 30 mpg (miles per gallon) decides to carry out a fuel efficiency test. Six nonprofessional drivers are selected, and each one drives a car from Phoenix to Los Angeles. The resulting fuel efficiencies
=+rate higher than 40%. To investigate this theory, a distributor is fitted with an eye patch. Of the 200 questionnaires distributed by this individual, 109 were returned. Does this strongly suggest that the response rate in this situation exceeds the rate in the past? State and test the
=+10.90 Past experience has indicated that the true response rate is 40% when individuals are approached with a request to fill out and return a particular questionnaire in a stamped and addressed envelope. An investigator believes that if the person distributing the questionnaire is stigmatized
=+b. Suppose that it had previously been believed that mean consumption was at most 200 mg. Does the given information contradict this prior belief? Test the appropriate hypotheses at significance level .10.
=+a. Does it appear plausible that the population distribution of daily caffeine consumption is normal? Is it necessary to assume a normal population distribution to test hypotheses about the value of the population mean consumption? Explain your reasoning.
=+10.89 The article “Caffeine Knowledge, Attitudes, and Consumption in Adult Women” (Journal of Nutrition Education [1992]: 179–184) reported the following summary statistics on daily caffeine consumption for a random sample of adult women: n 5 47, mg, s 5 235 mg, and the data values ranged
=+Which of the symbols would be used to code for each of the following P-values?a. .037c. .072b. .0026d. .0003
=+10.86 When a published article reports the results of many hypothesis tests, the P-values are not usually given.Instead, the following type of coding scheme is frequently used: *p , .05, **p , .01, ***p , .001, ****p , .0001.
=+Does your conclusion change if a 5 .01 is used?
=+white represents “innocence, purity, honesty, and cleanliness.”) A random sample of 400 cars purchased during this period in a certain metropolitan area resulted in 100 cars that were white. Does the proportion of all cars purchased in this area that are white appear to differ from the
=+10.85 White remains the most popular car color in the United States, but its popularity appears to be slipping.According to an annual survey by DuPont (Los Angeles Times, February 22, 1994), white was the color of 20% of the vehicles purchased during 1993, a decline of 4% from the previous year.
=+California). A random sample of 750 local residents included 560 who strongly opposed hunting on the bay.Does this sample provide sufficient evidence to conclude that the majority of local residents oppose hunting on Morro Bay? Test the relevant hypotheses using a 5 .01.
=+10.83 Duck hunting in populated areas faces opposition on the basis of safety and environmental issues. The San Luis Obispo Telegram-Tribune (June 18, 1991) reported the results of a survey to assess public opinion regarding duck hunting on Morro Bay (located along the central coast of x
=+c. If a significance level of .05 or .01 were used instead of .10 in the test of Part (b), would you still reach the same conclusion? Explain.
=+b. Is there convincing evidence that the mean salary for all female MBA graduates is above $100,000? Test using a 5 .10.
=+a. Test the hypothesis that the mean salary of male MBA graduates from this school was in excess of $100,000 in 1996.
=+10.82 According to the article “Workaholism in Organizations: Gender Differences” (Sex Roles [1999]: 333–346), the following data were reported on 1996 income for random samples of male and female MBA graduates from a certain Canadian business school:N s Males 258 $133,442 $131,090
=+10.81 Are young women delaying marriage and marrying at a later age? This question was addressed in a report issued by the Census Bureau (Associated Press, June 8, 1991). The report stated that in 1970 (based on census results) the mean age of brides marrying for the first time was 20.8 years.
=+and a sample standard deviation of 16.3 kg. Is there sufficient evidence to conclude that the mean weight for nontop-20 starters is less than 105, the known value for top20 teams?
=+Sport [1990]: 395–401) reported on physical characteristics of Division I starting football players in the 1988 football season. Information for teams ranked in the top 20 was easily obtained, and it was reported that the mean weight of starters on top-20 teams was 105 kg. A random sample of
=+10.80 Speed, size, and strength are thought to be important factors in football performance. The article “Physical and Performance Characteristics of NCAA Division I Football Players” (Research Quarterly for Exercise and
=+a GPA below 3.0 at the end of their first year (“Who Loses HOPE? Attrition from Georgia’s College Scholarship Program,” Southern Economic Journal [1999]: 379–390). Do these data provide convincing evidence that a majority of students at Ivan Allen College who enroll with a HOPE
=+Technology (social science and humanities majors) in 1996 who had a B average going into college, 53.2% had
=+10.79 The state of Georgia’s HOPE scholarship program guarantees fully paid tuition to Georgia public universities for Georgia high school seniors who have a B average in academic requirements as long as they maintain a B average in college. Of 137 randomly selected students enrolling in the
=+10.78 The same survey described in Exercise 10.77 also asked the individuals in the sample what they thought was their best chance to obtain more than $500,000 in their lifetime. Twenty-eight percent responded “win a lottery or sweepstakes.” Does this provide convincing evidence that more
=+b. The article went on to state that of the 110 nonsmoking 18- to 19-year-olds, only 38.2% had been approached to buy cigarettes for an underage smoker. Is there evidence that less than half of nonsmoking 18- to 19-year-olds have been approached to buy cigarettes?
=+a. Is there convincing evidence that fewer than half of 18-to 19-year-olds have been approached to buy cigarettes by an underage smoker?
=+10.76 According to the article “Which Adults Do Underage Youth Ask for Cigarettes?” (American Journal of Public Health [1999]: 1561–1564), 43.6% of the 149 18- to 19-year-olds in a random sample have been asked to buy cigarettes for an underage smoker.
=+the authors of the article, the credit card industry asserts that at most 50% of college students carry a credit card balance from month to month. However, the authors of the article report that, in a random sample of 310 college students, 217 carried a balance each month. Does this sample
=+10.74 The article “Credit Cards and College Students:Who Pays, Who Benefits?” (Journal of College Student Development [1998]: 50–56) described a study of credit card payment practices of college students. According to
=+political candidate has decided to support legalization of casino gambling if he is convinced that more than twothirds of U.S. adults approve of casino gambling. USA Today (June 17, 1999) reported the results of a Gallup poll in which 1523 adults (selected at random from households with
=+10.73 A number of initiatives on the topic of legalized gambling have appeared on state ballots. Suppose that a
=+they have a higher than average risk of cancer. Do these data suggest that p, the true proportion of smokers who view themselves as being at increased risk of cancer is in fact less than .5, as claimed by the authors of the paper?Test the relevant hypotheses using a 5 .05.
=+10.72 The authors of the article “Perceived Risks of Heart Disease and Cancer Among Cigarette Smokers” (Journal of the American Medical Association [1999]: 1019–1021)expressed the concern that a majority of smokers do not view themselves as being at increased risk of heart disease or
=+e. Are the results of your simulation and analysis consistent with the statement that the statistic has a standard normal (z) distribution and the statistic t 5 has a t distribution? Explain.
=+these percentiles compare to those of the distributions displayed in the histograms? (Hint: Sort the 200 z values—in MINITAB, choose “Sort” from the Manip menu. Once the values are sorted, percentiles from the histogram can be found by counting in 10 [which is 5% of 200] values from either
=+d. The z and t histograms are based on only 200 samples, and they only approximate the corresponding sampling distributions. The 5th percentile for the standard normal distribution is 21.645 and the 95th percentile is 11.645.For a t distribution with df 5 5 2 1 5 4, the 5th and 95th percentiles
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