PROBLEM 1. A local university administers a comprehensive examination to the candidates for B.S. degrees in Business Administration. Five examinations are selected at random and scored. The scores are shown below. Grades 94 72 93 54 77 Develop a 98% confidence interval estimate for the mean of the population. Assume the population is normally distributed. ANS: 50.29 to 105.71 PTS: 1 TOP: Interval Estimation 2. A random sample of 87 airline pilots had an average yearly income of $99,400 with a standard deviation of $12,000. a. If we want to determine a 95% confidence interval for the average yearly income, what is the value of t? b. Develop a 95% confidence interval for the average yearly income of all pilots. ANS: a. 1.988 b. $96,842.37 to $101,957.60 PTS: 1 TOP: Interval Estimation 3. A random sample of 81 credit sales in a department store showed an average sale of $68.00. From past data, it is known that the standard deviation of the population is $27.00. a. Determine the standard error of the mean. b. With a 0.95 probability, what can be said about the size of the margin of error? c. What is the 95% confidence interval of the population mean? ANS: a. 3.0 b. 5.88 c. $62.12 to $73.88 PTS: 1 TOP: Interval Estimation 4. You are given the following information obtained from a sample of 5 observations taken from a population that has a normal distribution. 94 72 93 54 77
Develop a 98% confidence interval estimate for the mean of the population. ANS: 50.29 to 105.71 PTS: 1 TOP: Interval Estimation 5. Many people who bought X-Game gaming systems over the holidays have complained that the systems they purchased were defective. In a sample of 1200 units sold, 18 units were defective. a. Determine a 95% confidence interval for the percentage of defective systems. b. If 1.5 million X-Games were sold over the holidays, determine an interval for the number of defectives in sales. ANS: a. 0.00812 to 0.02188 (rounded) b. 12,184 to 32,816 PTS: 1 TOP: Interval Estimation 6. Choo Choo Paper Company produces papers of various thickness. A random sample of 256 cuts had a mean thickness of 30.3 mils with a standard deviation of 4 mils. Develop a 95% confidence interval for the mean thickness of the population. ANS: 29.81 to 30.79 PTS: 1 TOP: Interval Estimation 7. The average monthly electric bill of a random sample of 256 residents of a city is $90 with a standard deviation of $24. a. Construct a 90% confidence interval for the mean monthly electric bills of all residents. b. Construct a 95% confidence interval for the mean monthly electric bills of all residents. ANS: a. 87.5325 to 92.4675 b. 87.06 to 92.94 PTS: 1 TOP: Interval Estimation 8. In a random sample of 400 registered voters, 120 indicated they plan to vote for Candidate A.
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