1. A trucking company continuously monitors the tread remaining on its fleet of truck tires. The firm knows that standard deviation is 0.1 cm. Suppose a sample of 80 tires were obtained, and the mean tread was 2.2 cm. Construct a 99% confidence interval. The company's operations manager knows that flat tires occur more often when the tread is below 1.0 cm. At what sample mean (and higher) should the company reasonably expect minimal flat tires, based on a 95% confidence interval?
2. Monthly expenses for an advertising agency were obtained for the previous year. The sample of 12 expenses showed a mean of $196,000, with a standard deviation of $45,000. The office manager is budgeting for monthly expenses, and would like to know if it is reasonable to expect expenses to be below $250,000. Construct a 95% confidence interval to justify if $250,000 is reasonable.
3. An online business consulting firm provides its service on a hourly basis. In the previous 15 months, the business had the following number of hours billed for its services.( Hours billed: 212 389 457 505 740 678 987 573 761 812 933 691 558 575 872)
a. What is the point estimate of the population mean?
b. Construct a 90% confidence interval.
4. As the operator of an e-commerce web site, you are interested in monitoring the average time spent on the site. How large of a sample of usage times should be obtained, provided your allowable error is 30 seconds. Based on a long history, you know the standard deviation of usage times is 5 minutes. Assume a 90% level of confidence.