1. A project manager on reviewing a random sample of maintenance projects discovers that the mean development time for the sample is 350 days with a standard deviation of 100 days.
   Note: Assume development time is normally distributed.
   1. Provide point estimates for the population parameters mu(y) and sigma(y).
   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. Twenty six projects were reviewed. Construct and interpret a 95% confidence interval for mean development time.
   
   
2. A leading newspaper columnist publishes an article that states that the mean income of tenured faculty at Universities throughout the Chicago area is $62,500. A DePaul statistician disagrees, believes that the columnist is ill-informed, and claims that mean income is actually less than the columnist claims.
   1. State the null and alternative hypotheses.
   2. The statistician interviews 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
        
      Determine the p-value for the hypotheses for part a. above and comment on its significance.
   3. Consider the statistics obtained for part b. above. The statistician would like to predict income from years of tenure. Given these statistics, and assuming that simple linear regression is appropriate, complete the following:
      1. Derive the equation of the regression line.
      2. Interpret the slope of the regression equation. Is the intercept meaningful?.
   
   
3. You have been asked to use simple linear regression 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. Given these summary statistics, and assuming the correlation coefficient is 0.9891 answer the following:
   1. Interpret the correlation coefficient.
   2. Derive the regression equation.
   3. Interpret the coefficients of the regression equation.
   
   
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.