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737: Time/CNN voter polls monitored public opinion for the presidential candidates during the 2000 presidential election campaign. One Time/CNN poll conducted by Yankelovich Partners, Inc., used a sample of 589 likely voters. Assume the population proportion for a presidential candidate is p = .50. Let be the sample proportion of likely voters favoring the presidential candidate. a. Show the sampling distribution of . b. What is the probability the Time/CNN poll will provide a sample proportion within ± .04 of the population proportion? c. What is the probability the Time/CNN poll will provide a sample proportion within ± .03 of the population proportion? d. What is the probability the Time/CNN poll will provide a sample proportion within ± .02 of the population proportion? 738: Roper ASW conducted a survey to learn about American adults’ attitudes toward money and happiness. 56% of the respondents said they balance their checkbook at least once a month. a. Suppose a sample of 400 American adults were taken. Show the sampling distribution of the proportion of adults who balance their checkbook at least once a month . b. What is the probability that the sample proportion will be within ± .02 of the population proportion? c. What is the probability that the sample proportion will be within ± .04 of the population proportion? 740: The Grocery Manufacturers of America reported that 76% of consumers read the ingredients listed on a product’s label. Assume the population proportion is p = .76 and a sample of 400 consumers is selected from the population. a. Show the sampling distribution of where is the proportion of the sampled consumers who read the ingredients listed on a product’s label. b. What is the probability that the sample proportion will be within ± .03 of the population proportion? c. Answer part (b) for a sample of 750 consumers. 82: A simple random sample of 50 items from a population with σ = 6 resulted in a sample mean of 32. a. Provide a 90% confidence interval for the population mean. b. Provide a 95% confidence interval for the population mean. c. Provide a 99% confidence interval for the population mean. 85: In an effort to estimate the mean amount spent per customer for dinner at a major Atlanta restaurant, data were collected for a sample of 49 customers. Assume a population standard deviation of $5. a. At 95% confidence, what is the margin of error? b. If the sample mean is $24.80, what is the 95% confidence interval for the population mean? 87: A survey of small businesses with Web sites found that the average amount spent on a site was $11,500 per year (Fortune, March 5, 2001). Given a sample of 60 businesses and a population standard deviation of σ = $4000, what is the margin of error? Use 95% confidence. What would you recommend if the study required a margin of error of $500? 814: A simple random sample with n = 54 provided a sample mean of 22.5 and a sample standard deviation of 4.4. a. Develop a 90% confidence interval for the population mean. b. Develop a 95% confidence interval for the population mean. c. Develop a 99% confidence interval for the population mean. d. What happens to the margin of error and the confidence interval as the confidence level is increased? 820: Is your favorite TV program often interrupted by advertising? CNBC presented statistics on the average number of programming minutes in a halfhour sitcom (CNBC, February 23, 2006). The following data (in minutes) are representative of their findings. Click here for Data in Excel File Format 21.06 22.24 20.62 21.66 21.23 23.86 23.82 20.30 21.52 21.52 21.91 23.14 20.02 22.20 21.20 22.37 22.19 22.34 23.36 23.44 Assume the population is approximately normal. Provide a point estimate and a 95% confidence interval for the mean number of programming minutes during a halfhour television sitcom. 821: Consumption of alcoholic beverages by young women of drinking age has been increasing in the United Kingdom, the United States, and Europe. Data (annual consumption in liters) consistent with the finding reported in The Wall Street Journal article are shown for a sample of 20 European young women. Click here for Data in Excel File Format 266 82 199 174 97 170 222 115 130 169 164 102 113 171 0 93 0 93 110 130 Assuming the population is roughly symmetric; construct a 95% confidence interval for the mean annual consumption of alcoholic beverages by European young women. 827: Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $30,000 and $45,000. Assume that a 95% confidence interval estimate of the population mean annual starting salary is desired. What is the planning value for the population standard deviation? How large a sample should be taken if the desired margin of error is a. $500? b. $200? c. $100? d. Would you recommend trying to obtain the $100 margin of error? Explain. 828: An online survey by ShareBuilder, a retirement plan provider, and Harris Interactive reported that 60% of female business owners are not confident they are saving enough for retirement(SmallBiz, Winter 2006). Suppose we would like to do a followup study to determine how much female business owners are saving each year toward retirement and want to use $100 as the desired margin of error for an interval estimate of the population mean. Use $1100 as a planning value for the standard deviation and recommend a sample size for each of the following situations. a. A 90% confidence interval is desired for the mean amount saved. b. A 95% confidence interval is desired for the mean amount saved. c. A 99% confidence interval is desired for the mean amount saved. d. When the desired margin of error is set, what happens to the sample size as the confidence level is increased? Would you recommend a 99% confidence level be used by Smith Travel Research? Discuss. 92: The manager of an automobile dealership is considering a new bonus plan designed to increase sales volume. Currently, the mean sales volume is 14 automobiles per month. The manager wants to conduct a research study to see whether the new bonus plan increases sales volume. To collect data on the plan, a sample of sales personnel will be allowed to sell under the new bonus plan for a onemonth period. a. Develop the null and alternative hypotheses most appropriate for this research situation b. Comment on the conclusion when Ho cannot be rejected c. Comment on the conclusion when Ho can be rejected. 93: A production line operation is designed to fill cartons with laundry detergent to a mean weight of 32 ounces. A sample of cartons is periodically selected and weighed to determine whether underfilling or overfilling is occurring. If the sample data lead to a conclusion of underfilling or overfilling, the production line will be shut down and adjusted to obtain proper filling. a. Formulate the null and alternative hypotheses that will help in deciding whether to shut down and adjust the production line. b. Comment on the conclusion and the decision when Ho cannot be rejected. c. Comment on the conclusion and the decision when Ho can be rejected. 910: Consider the following hypothesis test. Ho: μ ≤ 25 Ha: μ > 25 A sample of 40 provided a sample mean of 26.4. The population standard deviation is 6. a. Compute the value of the test statistic. b. What is the pvalue? c. At α = .01, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion? 914: Consider the following hypothesis test: Ho: μ = 22 Ha: μ ≠ 22 A sample of 75 is used and the population standard deviation is 10. Compute the pvalue and state your conclusion for each of the following sample results. Use α = .01. a. xbar = 23 b. xbar = 25.1 c. xbar = 20 916: Reis Inc., a New York real estate research firm, tracks the cost of apartment rentals in the United States. In mid2002, the nationwide mean apartment rental rate was $895 per month. Assume that, based on the historical quarterly surveys, a population standard deviation of σ = $225 is reasonable. In a current study of apartment rentals rates, a sample of 180 apartments nationwide provided the apartment rental rates shown in data in Excel file Format Click here for Data in Excel File Format. Do the sample data enable Reis to conclude that the population mean apartment rental rate now exceeds the level reported in 2002? a. State the null and alternative hypotheses. b. What is the pvalue? c. At α = .01, what is your conclusion? d. What would you recommend Reis consider doing at this time? 917: Wall Street securities firms paid out record yearend bonuses of $125,500 per employee for 2005. Suppose we would like to take a sample of employees at the Jones & Ryan securities firm to see whether the mean yearend bonus us different from the reported mean of $125,500 for the population.
919: In 2001, the U.S. Department of Labor reported the average hourly earnings for U.S. production workers to be $14.32 per hour. A sample of 75 production workers during 2003 showed a sample mean of $14.68 per hour. Assuming the population standard deviation σ = $1.45, can we conclude that an increase occurred in the mean hourly earnings since 2001? Use α = .05. 923: Consider the following hypothesis test. Ho: μ ≤ 12 Ha: μ > 12 A sample of 25 provided a sample mean xbar = 14 and sample standard deviation s = 4.32. a. Compute the value of the test statistic. b. What does the t distribution table (Table 2 in Appendix B) to compute a range for the pvalue? c. At α = .05, what is your conclusion? d. What is the rejection rule using the critical value? What is your conclusion? 926: Consider the following hypothesis test. Ho: μ = 100 Ha: μ ≠ 100 A sample of 65 is used. Identify the pvalue and state your conclusion for each of the following sample results. Use α = .05. a. xbar = 103 and s = 11.5 b. xbar = 96.5 and s = 11.0 c. xbar = 102 and s = 10.5 928: A shareholder’s group, in lodging a pretest, claimed that the mean tenure for a chief executive office (CEO) was at least nine years. A survey of companies reported in The Wall Street Journal found a sample mean tenure of x bar = 7.27 years for CEOs with a standard deviation of s =6.38 years.
931: Raftelis Financial Consulting reported that the mean quarterly water bill in the United States is $47.50. Some water systems are operated by public utilities, whereas other water systems are operated by private companies. An economist pointed out that privatization does not equal competition and that monopoly powers provided to public utilities are now being transferred to private companies. The concern is that consumers end up paying higherthanaverage rates for water provided by private companies. The water system for Atlanta, Georgia, is provided by a private company. A sample of 64 Atlanta consumers showed a mean quarterly water bill of $51 with a sample standard deviation of $12. At α = .05, does the Atlanta sample support the conclusion that aboveaverage rates exist for this private water system? What is your conclusion? ========================================================================= 127: Would you expect more reliable cars to cost more? Consumer Reports rated 15 upscale sedans. Reliability was rated on a 5point scale: poor (1), fair (2), good (3), very good (4), and excellent (5). The price and reliability rating for each of the 15 cars are shown. Click here for Data in Excel File Format a. Develop a scatter diagram for these data with the reliability rating as the independent variable. b. Develop the least squares estimated regression equation. c. Based upon your analysis, do you think more reliable cars cost more? Explain. d. Estimate the price for an upscale sedan that has an average reliability rating. 1210: Bergans of Norway has been making outdoor gear since 1908. The following data show the temperature rating (F°) and the price ($) for 11 models of sleeping bags produced by Bergans Click here for Data in Excel File Format a. Develop a scatter diagram for these data with temperature rating (F°) as the independent variable. b. What does the scatter diagram develop in part (a) indicate about the relationship between temperature rating (F°) and price? c. Use the least squares method to develop the estimated regression equation. d. Predict the price for a sleeping bag with a temperature rating (F°) of 20. 1220: Consumer Reports provided extensive testing and ratings for more than 100 HDTVs. An overall score, based primary on picture quality, was developed for each model. In general, a higher overall score indicates better performance. The following data show the price and overall score for the ten 42inch plasma televisions. Click here for Data in Excel File Format
