1. A project manager on reviewing a sample of maintenance projects discovers that the mean development time for the sample is 350 days with a standard deviation of 100 days.
   

   1. Provide point estimates for the population parameters mu and sigma.
   2. Determine the percentage of maintenance projects that required more than 375 days for completion.
   3. The CIO questions the accuracy of the estimate of mean development time. Assume that 25 projects were reviewed. Construct and interpret a 95% confidence interval for mean development time.
   
   
2. A leading newspaper columnist contends that the mean income of tenured faculty at Universities throughout the Chicago area is $62,500. A DePaul statistician believes that the columnist is ill-informed and that mean income is actually less than he claims. The statistician decides to investigate.

   1. State the null and alternative hypotheses.
   2. The statistician collects a random sample of 100 tenured faculty from several Universities in Chicago and discovers that the mean is $60,000 and the standard deviation is $10,000. Given these statistics, and your hypotheses, conduct a test of hypotheses. Remember to comment on the columnists point of view.
   
   
3. The director of applications development at a local bank submits a Y2K budget to the CIO. The CIO notices that the director has used $2.10 as the mean cost per line of code. The CIO believes that this cost is too high and decides to conduct an experiment to resolve the issue.

   1. State the null and alternative hypotheses.
   2. The CIO discovers that the mean cost per line of code for a random sample of 25 programs is $2.04 and the standard deviation is $0.30. Conduct a test of significance and comment on the director's claim.
   3. Given your comment for part b. briefly explain why a point estimate for the population mean is (or is not) appropriate.