1. An article discussed the changes that banks in a certain country are making to the way they calculate the minimum payment due on credit card balances. The changes are being pushed by regulators in the country. In the past, minimum payments were set at about 3% of the outstanding balance. Each credit card issuer is making its own changes. Suppose that a large bank in the country is in the process of considering what changes to make. It wishes to survey its customers to estimate the mean percent payment on their outstanding balance that customers would like to see. The bank wants to construct a 90% confidence interval estimate with a margin of error of plus or minus 0.2 percent. A pilot sample of n=40 customers showed a sample standard deviation of 1.4%. How many more customers does the bank need to survey in order to construct the interval estimate? The bank needs to survey ____ more customers. 2. A study that randomly surveyed 3,500 households found that 46% of households have funded at least one IRA rollover from an employer-sponsored retirement plan. Suppose a recent random sample of 50 households in a metropolitan area was taken and respondents were asked whether they had ever funded an IRA account with a rollover from an employer-sponsored retirement plan. The results are available in the accompanying table. Complete parts a through c below. a. Based on the random sample, what is the best point estimate for the proportion of all households in the metropolitan area that have ever funded an IRA account with a rollover from an employer-sponsored retirement plan? The best point estimate for the proportion is ____. (Type an integer or a decimal.) b. Construct a 99% confidence interval estimate for the true population proportion of households in the metropolitan area that had ever funded an IRA account with a rollover from an employer-sponsored retirement plan _____. (Round to three decimal places as needed. Use ascending order.) c. If the sponsors of the study found that the margin of error was too high, what could they do to reduce it if they were not willing to change the level of confidence? The sponsors could a. increase b. decrease the a. population proportion. b. sample proportion. c. sample size. RespondentResponse 1 No 2 Yes 3 Yes 4 No 5 No 6 Yes 7 Yes 8 No 9 Yes 10 No 11 Yes 12 Yes 13 No 14 No 15 No Respondent Response 25 Yes 26 No 27 No 28 No 29 No 30 No 31 No 32 Yes 33 No 34 No 35 No 36 No 37 Yes 38 Yes 39 No Respondent Response 49 Yes 50 No 16 No 17 No 18 No 19 No 20 No 21 No 22 Yes 23 Yes 24 Yes Confidence Level 80% 90% 95% 99% 40 No 41 No 42 Yes 43 Yes 44 Yes 45 No 46 Yes 47 Yes 48 No Critical Value z=1.28 z=1.645 z=1.96 z=2.575 4. An article points out that some companies have started to feature female models who are not the traditional rail-thin women who have graced billboards and magazine covers for the last 20-25 years. These new models, called "real people," are still very athletic and represent what one spokeswoman calls "what is real" as opposed to "what is ideal." The article also reports on a survey of 1,000 women, in which 74% of the respondents said they were satisfied with what they see in the mirror. A company's managers would like to use these data to develop a 90% confidence interval estimate for the true proportion of all women who are satisfied with their bodies. Develop and interpret the 90% confidence interval estimate. The confidence interval estimate is ____ ____. (Round to three decimal places as needed.) Interpret the confidence interval estimate. A. With 90% confidence, the true proportion of all women who are satisfied with their bodies is within the interval found in part a. B. With 90% confidence, the true proportion of all women who are satisfied with their bodies is within 3 margins of error of the sample proportion. C. With 90% confidence, the sample proportion of all women who are satisfied with their bodies is equal to the true proportion. D. With 90% confidence, the sample proportion of all women who are satisfied with their bodies is within the interval found in part a. 5. An airline is considering charging a two-tiered rate for checked bags based on their weight. Before deciding at what weight to increase the rate, the airline wishes to estimate the mean weight per bag checked by passengers. It wants the estimate to be within plus or minus 0.25 pounds of the true population mean. A pilot sample of checked bags produced the results shown below. 47 47 43 49 43 39 44 38 38 45 46 35 40 49 49 40 41 49 48 43 a. What sample size should the airline use if it wants to have 95% confidence? b. Suppose the airline managers do not want to take as large a sample as the one determined in part a. What general options do they have to lower the required sample size? a. The sample size must be at least ____. (Round up to the nearest whole number.) b. What could the managers do to lower the required sample size? Select all that apply. A. Reduce the level of confidence B. Increase the population standard deviation C. Use a larger pilot sample D. Increase the margin of error 6. A survey concluded that men, of any age, are twice as likely as women to play console video games. The survey was based on a sample of men and women ages 12 and older. In a sample of 100 men and 100 women for the 18- to 34-year-old age group, there were 47 men and 21 women who played console video games. a. Calculate a 99% confidence interval for both the male and female responses. b. Using the confidence intervals in part a, provide the minimum and maximum ratios of the population proportions. c. Do your analyses in parts a and b substantiate the statement that men in this age group are twice as likely to play console video games? Support your assertions. a. The confidence interval estimate for men is ____ ____. (Round to three decimal places as needed.) The confidence interval estimate for women is ____. (Round to three decimal places as needed.) b. The minimum ratio of male gamers to female gamers is. ____ (Round to three decimal places as needed.) The maximum ratio of male gamers to female gamers is. ____ (Round to three decimal places as needed.) c. Do your analyses in parts a and b substantiate the statement that men in this age group are twice as likely to play console video games? A. No, because the minimum ratio shows that there are more than twice as many men as women that play console video games. B. Yes, because the ratios show that it is possible that there are twice as many men as women that play console video games. C. No, because the maximum ratio shows that there are less than twice as many men as women that play console video games. 7. A random sample of size 120 taken from a population yields a proportion equal to 0.33. Complete parts a through d below. a. Determine if the sample size is large enough so that the sampling distribution can be approximated by a normal distribution. Since np overbar= ____ and n(1p overbar p)= ____, the sample size a. is b. is not large enough. (Round to the nearest whole number as needed.) b. Construct a 95% confidence interval for the population proportion.____ (Round to three decimal places as needed. Use ascending order.) c. Interpret the confidence interval calculated in part b. Which statement below correctly interprets the confidence interval? A. There is a 0.950.95 probability that the sample proportion is in the interval. B. There is a 0.950.95 probability that the population proportion is in the interval. C. Of all the possible population proportions, 9595% are in the interval. D. There is 95% confidence that the population proportion is in the interval. d. Produce the margin of error associated with this confidence interval. e=____ (Round to three decimal places as needed.) 8. At issue is the proportion of people in a particular country who do not have health care insurance coverage. A simple random sample of 400 people was asked if they have insurance coverage, and 120 replied that they did not have coverage. Based on these sample data, determine the 95% confidence interval estimate for the population proportion. The confidence interval is ____ ____. (Round to three decimal places as needed.) 9. The accompanying data set contains a random sample of 144 coffee drinkers in a certain country and measures the annual coffee consumption in kilograms for each sampled coffee drinker. A marketing research firm wants to use this information to develop an advertising campaign to increase coffee consumption. Complete parts a and b below. 3.5 5.5 6.2 6.6 7.1 7.8 3.8 5.5 6.2 6.6 7.1 7.8 4.4 5.6 6.2 6.6 7.1 7.8 4.5 5.6 6.2 6.7 7.2 7.9 4.6 5.7 6.2 6.7 7.2 7.9 4.6 5.7 6.3 6.7 7.2 7.9 4.7 5.7 6.3 6.7 7.3 7.9 4.7 5.7 6.3 6.8 7.3 7.9 4.8 5.8 6.3 6.8 7.3 7.9 4.8 5.8 6.3 6.8 7.4 7.9 5 5.9 6.3 6.8 7.5 8.1 5 5.9 6.4 6.8 7.5 8.1 5 6 6.4 6.8 7.5 8.3 5 6 6.4 6.8 7.5 8.3 5.2 6 6.5 6.8 7.5 8.4 5.3 6 6.5 6.8 7.5 8.5 5.3 6 6.5 6.9 7.5 8.6 5.3 6 6.5 6.9 7.5 8.8 5.3 5.3 5.3 5.4 5.4 5.4 5.4 6 6 6.1 6.1 6.1 6.1 6.1 6.5 6.5 6.6 6.6 6.6 6.6 6.6 6.9 6.9 6.9 6.9 6.9 7.1 7.1 7.5 7.6 7.6 7.6 7.7 7.7 7.8 10.1 _____ kg. (Round to four decimal places as needed.) b. Develop and interpret a 99% confidence interval estimate for the mean annual coffee consumption of coffee drinkers in this country. The 99% confidence interval is ____ kg. ____ kg. (Round to four decimal places as needed.) Interpret this interval. Choose the correct answer below. A. One can conclude that the population mean annual coffee consumption of coffee drinkers in this country falls between these two values 99% of the time. B. There is a 0.99 probability that the population mean annual coffee consumption of coffee drinkers in this country is between these two values. C. One can conclude with 99% confidence that the sample mean annual coffee consumption of coffee drinkers in this country is between these two values. D. One can conclude with 99% confidence that the population mean annual coffee consumption of coffee drinkers in this country is between these two values. 10. A company provides call center services for businesses. The company bills it clients either by the call or by the minute. The company is negotiating with a new client who wants to be billed by the minute. Before a contract is written, the company plans to receive a random sample of calls and record the minutes spent on the phone in order to estimate the mean call time. It wishes to develop a 96% confidence interval estimate for the population mean call time and wants this estimate to be within 0.18 minutes. The question is, how many calls should the company use in its sample? Since the population standard deviation is unknown, a pilot sample was taken by having three call centers each take 50 calls for a total pilot sample of 150 calls. The minutes for these calls are in the accompanying data table. Complete parts a and b below. a. How many additional calls will be needed to compute the desired confidence interval estimate for the population mean? At least _____ additional calls will be needed. (Round up to the nearest whole number as needed.) b. In the event that the managers at the company want a smaller sample size, what options do they have? Discuss in general terms. The company has the option to a. reduce b. increase the confidence level or a. reduce b. increase the margin of error or some combination of the two. Call Center 1 Call Center 2 Call Center 3 11.82 11.72 17.72 9.64 12.88 10.99 13.42 14.78 13.48 16.11 9.48 20.91 10.17 12.03 13.56 10.42 18.24 12.16 12.02 12.65 18.89 13.03 16.05 16.84 7.81 9.26 18.16 10.14 8.81 13.78 17.18 9.21 15.69 10.77 12.38 13.46 15.69 14.45 16.92 11.67 14.76 17.28 15.18 12.21 10.27 7.74 9.24 12.64 18.03 8.28 12.84 11.74 12.38 21.46 15.74 12.45 20.29 9.85 10.86 13.47 10.75 15.89 17.13 7.39 10.88 16.29 11.29 10.52 15.57 5.75 19.21 18.82 10.62 7.33 14.98 13.59 11.29 12.12 12.31 12.91 9.86 9.57 10.93 17.75 16.17 12.34 18.27 10.11 11.79 16.42 12.54 9.23 15.87 12.23 12.09 14.63 14.54 15.59 17.23 17.92 15.51 18.18 8.69 12.42 14.37 16.17 13.71 13.81 9.42 15.32 8.83 11.23 12.81 18.02 16.31 15.59 18.88 12.93 14.18 15.74 14.79 14.78 16.24 9.16 10.58 11.62 8.32 14.89 7.36 15.22 13.24 10.38 11.87 12.67 16.08 15.03 13.13 12.99 11.87 17.06 10.43 21.44 19.08 20.73 12.97 16.96 13.63 15.32 13.81 15.37 As a follow-up to a report on gas consumption, a consumer group conducted a study of SUV owners to estimate the mean mileage for their vehicles. A simple random sample of 83 SUV owners was selected, and the owners were asked to report their highway mileage. The results that were summarized from the sample data were x overbar=18.2 mpg and s=5.4 mpg. Based on these sample data, compute and interpret a 90% confidence interval estimate for the mean highway mileage for SUVs. The 90% confidence interval is ____ mpg _____ mpg. (Round to one decimal place as needed. Use ascending order.) Interpret this interval. Choose the correct answer below. A. One can conclude that the true mean highway mpg for SUVs will fall in this range 90% of the time. B. One can conclude with 90% confidence that the true mean highway mpg for SUVs is in this range. C. There is a 0.90 probability that the true mean highway mpg for SUVs falls in this range. D. One can conclude with 90% confidence that the sample mean highway mpg for SUVs is in this range. Compute the 90% confidence interval estimate for the population proportion, p, based on a sample size of 100 when the sample proportion, p overbarp, is equal to 0.39. __________ ____________________ Confidence Level 80% 90% 95% 99% Critical Value z=1.28 z=1.645 z=1.96 z=2.575