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. Estimate 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.
   5. The CIO claims that mean development time is 300 days. Comment on the CIO's claim
   
   
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 appropriate population mean is significantly different from the columnists claim.
   2. Derive the p-value for the hypotheses for part a. above and comment on the significance of the test.
   3. If income is the dependent variable and years of tenure the independent variable, derive the equation for the regression line of income as a function of years of tenure
   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 a positive linear relationship between the dependent and independent variables, answer the following:
      1. Complete this fragment of the Analysis of Variance report produced by proc reg.
      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.