## Statistics 101 Problem Set #6 Fall 1999

This homework is to be done in groups of up to three people. It is due on the last day of class.

Write a report to respond to the following situation. The report should consist of:

1. An executive summary that states your conclusions
2. A nontechnical report of your basic results
3. Technical backup, including any relevant output and graphics

The executive summary should be a summary, not an introduction. It should highlight results, not your actions. The report should be more detailed but should avoid technical language such as skewness. The technical backup is an appendix, in effect.

This is the Case at the end of Chapter 2 of H&O, pp. 63-4. The data may be downloaded from the web. You can find the data (meat.jmp) on the Stat 101 main page.

A meat packer sells frozen "12 ounce" steaks to restaurants. The meat is cut, frozen, and packaged on two production lines called (not-too- imaginatively) the Left and Right lines. The target size for each steak is 12 ounces, but there is variability because of differences in meat density, slight differences in cut, slight differences in fat content, and several other factors. Each steak is visually inspected and also weighed by a rough scale along the production line; the scale is supposed to reject any steak that weighs less than 11.5 ounces and set aside any steak that weighs more than 12.6 ounces.

The production managers have noticed an increase in the number of 24-steak packages being rejected by customers for inadequate average weight. The managers traced the source of each rejected package and found that most had come from the Right line. They have written to you for help. "As you know, quality control picks 10 steaks each week from each line for careful testing. Before they're cooked, they're all weighed carefully. We've got weights for each line for the last 25 weeks. During the first 10 weeks, we were running at speeds well below capacity to make sure that our cutting was OK. The last 15 weeks, we've been running at nearly full capacity. What we can't figure out is that the average weights from the two lines are practically identical; if anything, the Right line averages a little heavier. So why are so many more of the Right line packages coming up short?" They enclosed the weights for each week's sample of 10 steaks.

Can you identify any difference between the Left and Right data that might explain the problem? Does the difference show up after the initial 10 weeks or during that period? Write a memorandum to the managers; they don't know any technical terms, so try to use ordinary English as much as possible.