1. A professional association reported that the mean annual household income of its members is $86,000. Assume this estimate of the mean household income is based on a sample of 100 households, and based on past studies, the population standard deviation is known to be $30,000. Develop a 90% confidence interval estimate of the population mean. Develop a 95% confidence interval estimate of the population mean. Develop a 99% confidence interval estimate of the population mean. Discuss what happens to the width of the confidence interval as the confidence level increases.

2. Contractors for a plumbing service submit weekly reports which list the customer contacts made during the week. A sample of 70 weekly reports showed a sample mean of 22.5 customer contacts per week. The sample standard deviation was 6.3.

Find the 90% confidence interval estimate of the population mean number of weekly customer contacts for the contractors. Find the 95% confidence interval estimate of the population mean number of weekly customer contacts for the contractors.