Page 1 of 9 ORMS 3310 Quiz ch8&9 V5 Take-Home Scatrons Due: At the beginning of class on Thursday April 1, 2010 Case 1: A simple random sample of 60 items from a population with σ = 12 resulted in a sample mean of 35 1. Which of the following statements is most unreasonable, not true, about confidence interval estimates of the population mean? a. A 90% confidence interval for the population mean is 35 ± 2.541 b. A 98% confidence interval for the population mean is 35 ± 3.61 c. A 99% confidence interval for the population mean is 35 ± 3.02 d. A 95% confidence interval for the population mean is 35 ± 3.036 Case 2: 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 64 customers. Assume a population standard deviation of $5. 2. Which of the following statements is most unreasonable, not true, about the effort to estimate the mean? a. At 90% confidence, the margin of error is 1.025 b. At 95% confidence, the margin of error is 1.225 c. At 98% confidence, the margin of error is 1.456 d. If the sample mean is $37.80, the 99% confidence interval for the population mean is 37.80 ± 1.613 e. If the sample mean is $37.80, the 95% confidence interval for the population mean is 37.80 ± 1.4 Case 3&4 : A survey of small businesses with Web sites found that the average amount spent on a site was $10,500 per year (Questions 3 & 4). 3. Which of the following statements is MOST unreasonable, false? a. If n= 100 businesses and σ = $4000, the margin of error associated with a 95% confidence interval is $784 b. If n= 64 businesses and σ = $4000, the margin of error associated with a 95% confidence interval is $780 c. If n= 64 businesses and σ = $4000, the margin of error associated with a 90% confidence interval is $820 d. If n= 100 businesses and σ = $3178.3, the margin of error associated with a 99% confidence interval is $820 e. Everything else being the same, the sample size n would need to be increased to reduce the margin of error. 4. Which of the following statements is MOST unreasonable, false? a. If n= 31 businesses and s = 4000 , the margin of error associated with a 95% confidence interval is $1467 b. If n= 41 businesses and s = $4000, the margin of error associated with a 90% confidence interval is $1052 c. If n= 31 businesses and s = $3000, the margin of error associated with a 95% confidence interval is $1100 d. If n= 41 businesses and s = $3000, the margin of error associated with a 99% confidence interval is $1267 e. If n= 41 businesses and s = $3000, the margin of error associated with a 90% confidence interval is $1053 Case 5: The American Association of Advertising Agencies records data on nonprogram minutes on half-hour, prime-time television shows. Representative data in minutes for a sample of 20 prime-time shows on major networks at 8:30 P.M. follow. (For question 5) 9.9 7.0 7.2 7.0 9.0 7.3 6.0 6.6 6.3 5.7 6.5 6.5 7.6 8.5 5.8 6.2 6.4 8.2 7.2 6.8 5. Assume a normal population and provide a point estimate and a 95% confidence interval for the mean number of non-program minutes on half-hour, prime-time television shows at 8:30 P.M. a. 20 ± 0.512 b. 7.085 ± 2.09 c. 20 ± 2.09 d. 7.085 ± 0.512 Case 6: Complaints about rising prescription drug prices caused the U.S. Congress to consider laws that would force pharmaceutical companies to offer prescription discounts to senior citizens without drug benefits. The House Government Reform Committee provided data on the prescription cost for some of the most widely used drugs. Assume the following data show a sample of the prescription cost in dollars for Zocor, a drug used to lower cholesterol. (For question 6) 110 112 115 125 100 130 104 126Page 2 of 9 6. Given a normal population, what is the 95% confidence interval estimate of the population mean cost for a prescription of Zocor? a. 115.25 ± 9.08 b. 8 ± 9.08 c. 8 ± 2.365 d. 115.25 ± 2.365 Case 7: Annual starting salaries for college graduates with degrees in business administration are generally expected to be between $25,000 and $35,000. Assume that a 90% confidence interval estimate of the population mean annual starting salary is desired. (For question 7) 7. Which of the following statements is most unreasonable, FALSE? a. The planning value for the population standard deviation is 2500 b. If the desired margin of error is $500, the required sample size should be 168. c. If the desired margin of error is $200, the required sample size should be 423. d. If the desired margin of error is $100, the required sample size should be 1691. e. To reduce the desired margin of error, the required sample size should be increased. Case 8: Smith Travel Research provides information on the one-night cost of hotel rooms throughout the United States. Use $3 as the desired margin of error and $22.50 as the planning value for the population standard deviation. (For question 8) 8. Which of the following statements is most unreasonable, FALSE? a. The required sample size for a 90% confidence interval estimate of the population mean cost of hotel rooms is 153 b. The required n for a 95% confidence interval estimate of the population mean cost of hotel rooms is 217 c. The required n for a 98% confidence interval estimate of the population mean cost of hotel rooms is 216 d. The required sample size for a 99% confidence interval estimate of the population mean cost of hotel rooms is 374 e. When the desired margin of error is fixed, the required sample size gets larger as the confidence level is increased Case 9: Consider the following hypothesis test. Ho: μ ≤ 25 Ha: μ > 25 A sample of 55 provided a sample mean of 26.4. The population standard deviation is 6. (For question 9) 9. At α = .01, what is your conclusion? a. Reject Ho. b. Do not reject Ho. c. There is not enough information to answer this question d. None of the above. Case 10: Consider the following hypothesis test: Ho: μ = 22 Ha: μ ≠ 22 A sample of 75 is used and the population standard deviation is 15. Compute the p-value and state your conclusion for the following sample results. Use α = .01. (For questions 10-11) 10. x-bar = 23 a. P-value = .2810, reject Ho. b. P-value = .4380, do not reject Ho. c. P-value = .5620, do not reject Ho. d. P-value = .2190, reject Ho. 11. x-bar = 25.1 a. P-value = .0367, do not reject Ho.