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Unformatted text preview: dealers of a large county are conducting a study to determine the proportion of car owners in the county who are considering the purchase of a new car within the next year. If the population proportion is believed to be no more than 0.15, how many owners must be included in a simple random sample if the dealers want to be 90% confident that the maximum likely error will be no more than 0.02? 4 PROBLEM # 7.16 Refer to Problem 7.15, suppose that (unknown to the dealers) the actual population proportion is really 0.35. If they use their estimated value (p=< 0.15) in determining the sample size and then conduct the study, will their maximum likely error be greater than, equal to, or less than 0.02? Why? PROBLEM # 7.17 The makers of Count Chocula breakfast cereal would like to determine, within 2 percentage points and with 99% confidence, the percentage of U.S. senior citizens who have Count Chocula for breakfast at least one a week. What sample size would you recommend? PROBLEM # 7.18 An airline has surveyed a simple random sample of air travelers to find out whether they would be interested in paying a higher fare in order to have access to e ­ mail during their flight. Of the 400 travelers surveyed, 80 said e ­mail access would be worth a slight extra cost. Construct a 95% confidence interval for the population proportion of air travelers who are in favor of the airline’s e ­mail idea. 1 2 3 4 5 6 A B z-Es tim ate of a Proportion S ample proportion S ample size Confidence le vel 0.20 4 00 0.95 C Confidence Interval E stimate 0.20 0 Lower confidence limit Upper confidence limit D E ± 0.0 39 0.1 61 0.2 39 5 PROBLEM # 7.19 “In surveying a simple random sample of 1000 employed adults, we found that 450 individuals felt they were underpaid by at least $ 3,000. Based on these results, we have 95% confidence that the proportion of the population of employed adults who share this sentiment is between 0.419 and 0.481.” For this summary statement, identify the a. point estimate of the population proportion. b. Confidence interval estimate for the population proportion. c. Confidence level and the confidence coefficient. Understanding the Basics: Suggested Problems from the Book. 7.1 z ­Based Confidence Intervals for a Population Mean: ! known: 7.2,7.4,7.6,7.8,7.10,7.12, 7.2 t ­Based Confidence Intervals for a Population Mean: ! unknown: 7.16,7.18,7.20,7.22,7.24 7.3 Sample Size Determination: 7.32,7.34,7.35,7.36,7.38 7.4 Confidence Intervals for a Population Proportion: 7.42,7.44,7.46,7.48,7.52,7.56 End of Chapter: 7.96,7.100,7.102,7.106 This statistical workbook is compiled from the following books: • • • • Keller, G. (2012). Statistics for management and economics. Mason: Cengage Learning. Weiers, R. M. (2011). Introduction to Business Statistics. Mason: Cengage Learning. (GMAC), F. t. (Ed.). (2005). GMAT  ­Quantitative Review. Oxford, UK: Blackwell. Gonick, L. W. (2005). The Cartoon Guide to Statistics (Vol. 1). HarperCollins. 6...
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