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 365 days for completion.
   3. One of these projects was completed in 250 days. What is the percentile rank of this project.
   4. The CIO questions the accuracy of the estimate of mean development time. Assume that 26 projects were reviewed. Compute 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. She collects a random sample of 100 tenured faculty from several Universities in Chicago and computes the following statistics from the sample:
   
   • income: mean = $60,000; SD = $10,000
   • years of tenure: mean = 20 years; SD = 5 years
   • correlation between income and years of tenure is 0.8
     
   1. State the null and alternative hypotheses required to determine if the columnists claim is reasonable.
   2. Determine the p-value for the hypotheses for part a. above and comment on its significance.
   3. The statistician decides that she would like to predict income from years of tenure. Derive the equation of the regression line.
   4. Interpret the slope of the regression equation. Is the intercept meaningful?.
   
   
3. You have been asked to use regression methods to derive an equation to predict the processing time of an encryption algorithm from document size. You are told that simple linear regression is appropriate for this problem.
   1. State the simple linear regression model.
   2. Given these summary statistics, and assuming the correlation coefficient is 0.9891 answer the following:
      1. Derive the regression equation.
      2. Interpret the coefficients of the regression equation.
      3. For documents of size 100 words, what proportion required more than 103 time units of processing.
   
   
4. 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 36 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.