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 standard deviation 100 days. If development time is normally distributed, answer the following:

    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.
    Note: Make and state necessary assumptions.

    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.
    Note: Make and state necessary assumptions.

    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.

  4. You are interested in the performance of an image compression algorithm. Let us say that, for a corpus of images, the mean compression time is 80ms with standard deviation 24.0ms.
    Consider samples of size 64 images that could be selected from this corpus. Given the sampling distribution of ybar, what proportion of samples would you expect to result in sample means less than 75ms.

  5. A software consulting firm asks an independent usability expert to evaluate a browser based GUI that they have developed for an electronic retailer. The retailer argues that, on average, for novice users, the new GUI is about the same as the existing interface. The consulting firm claims that the new interface will allow novice users to complete a standard task suite more quickly than the existing interface (i.e. on average 250 seconds).

    The expert selects a random sample of 25 novice users. He discovers that the mean task completion time for the proposed GUI is 245 seconds with standard deviation 50 seconds.
    Note: Make and state necessary assumptions.

    1. Conduct a test of hypotheses.
    2. Given your findings, is a point estimate appropriate? If so, provide a point estimate of task completion time as well as a 90% CI
    3. Determine the minimum sample size required to estimate the task completion time to an accuracy of 10 seconds with 99% confidence.

  6. An electronic retailer asks an independent usability expert to evaluate a browser based GUI proposed by a software consulting firm. The retailer doubts the claim that the new interface will allow novice users to complete tasks more quickly. The expert selects two random samples of novice users and assigns the proposed GUI to one group and the existing GUI to the other group. Each group has 36 users. He discovers that the mean task completion time for the proposed GUI is 250 seconds with standard deviation 71 seconds and for the existing GUI the mean time is 300 seconds with standard deviation 86 seconds. Conduct a test of hypotheses.