Chapter 8 Assignment 1

Problem 1: A random sample of 80 group leaders, supervisors, and similar personnel at General Motors revealed that, on average, they spent 6.5 years in a particular job before being promoted. The standard deviation using historical data was 1.7 years. Construct a 95% confidence interval. Explain which formulas you used and why?

Problem 2: As part of their business promotional package, the Milwaukee Chamber of Commerce would like an estimate of the mean cost per month to lease a one-bedroom apartment. A random sample of 40 apartments currently available for lease showed the mean cost per month was $340. The standard deviation of the sample was $25.

1. Develop a 98% confidence interval for the population mean.
2. Would it be reasonable to conclude that the population mean is $355 per month?
3. Explain which formulas you used and why? Is sigma known?

Problem 3: Marty Rowatti recently assumed the position of director of the YMCA of South Jersey. He would like some current data on how long current members of the YMCA have been members. To investigate, suppose he selects a random sample of 40 current members. The mean length of membership of those included in the sample is 8.32 years and the standard deviation is 3.07 years.

1. What is the mean of the population?
2. Develop a 90% confidence interval for the population mean.
3. The previous director, in the summary report she prepared as she retired, indicated the mean length of membership was now "almost 10 years." Does the sample information substantiate this claim? Cite evidence.

Problem 4: There are 20,000 eligible voters in York County, South Carolina. A random sample of 500 York County voters revealed 350 plan to vote to return Louella Miller to the state senate. Construct a 99% confidence interval for the proportion of voters in the county who plan to vote for Ms. Miller. From this sample information, can you confirm she will be re-elected?If only 275 plan to vote for Miller would you draw the same conclusion? Why?

Problem 5: You need to estimate the mean number of travel days per year for outside salespeople. The mean of a small pilot study was 150 days, with a populationstandard deviation of 14 days. If you must estimate the population mean within 2 days, how many outside salespeople should you sample? Use the 95% confidence level.

Problem 6: You plan to conduct a survey to find what proportion of the workforce has two or more jobs. You decide on the 95% confidence level and state that the estimated proportion must be within 2% of the population proportion. A pilot survey reveals that 5 of the 50 sampled hold two or more jobs. How many in the workforce should be interviewed to meet your requirements?