Statistics for Business and Economics Question Answers

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Chapter 8

29. The travel-to-work time for residents of the 15 largest cities in the United States is reported in the 2003 Information Please Almanac. Suppose that a preliminary simple random sample of residents of San Francisco is used to develop a planning value of 6.25 minutes for the population standard deviation.

If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 2 minutes, what sample size should be used? Assume 95% confidence.
Sample size=((1.96)^2 (〖6.25)〗^2)/2^2 =37.52  Sample size should be used 38.

If we want to estimate the population mean travel-to-work time for San Francisco residents with a margin of error of 1 minute, what sample size should be used? Assume 95% confidence.
Sample size=((1.96)^2 (〖6.25)〗^2)/1^2 =150.06  Sample size should be used 151.

37. Towers Perrin, a New York human resource consulting firm, conducted a survey of 1100 employees at medium-sized and large companies to determine how dissatisfied employees were with their jobs (The Wall Street Journal, January 29, 2003). Representative data are shown in the file JobSatisfaction. A response of Yes indicates the employee strongly disliked the current work experience.

What is the point estimate of the proportion of the population of employees who strongly dislike their current work experience?
¯p=473÷1100=0.43  Point estimate is 0.43

At 95% confidence, what is the margin of error?
Z_0.025 √((¯p(1-¯p))/n)=1.96√((0.43(1-0.43))/1100)=0.0293  Margin of error is 0.0293

What is the 95% confidence interval for the proportion of the population of employees who strongly dislike their current work experience?
¯p±0.0293  The 95% confidence interval is 0.4007 to 0.4593

Towers Perrin estimates that it costs employers one-third of an hourly employee’s annual salary to find a successor and as much as 1.5 times the annual salary to find a successor for a highly compensated employee. What message

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