Page#769 Critical Thinking

Was the draft lottery random?

In 1970, a lottery was used to determine who would be drafted into the U.S. Army. The 366 dates in the year were placed in individual capsules. First, the 31 January capsules were placed in a box: then the 29 February capsules were added and the two months were mixed. Then the 31 March capsules were added and the three months were mixed. This process continued until all months were included. The first capsule selected was September 14, so men born on that date were drafted first. The accompanying list shows the 366 dates in the order of selection.

1. Use the runs test to test the sequence for randomness above and below the median of 183.5
2. Use the Kruskal-Wallis test to test the claim that the 12 months had priority numbers drawn from the same population.
3. Calculate the 12 monthly means. Then plot those 12 means on a graph (The horizontal scale lists the 12 months, and the vertical scale ranges from 100 to 260.) Note any pattern suggesting that the original priority numbers were not randomly selected.
4. Based on the results from parts (a), (b), and (c), decide whether this particular draft lottery was fair. Write a statement supporting your position that it was fair or explaining why you believe that it was not fair. If you decided that this lottery was unfair, describe a process for selecting lottery numbers that would have been fair.

P age#798 Critical Thinking

Are the Axial loads within statistical control?

Exercises 9 and 10 in Section 14-2 used process data from a New York company that manufactures 0.0109-in thick aluminum cans for a major beverage supplier. Refer to the data set below and conduct an analysis of the process data for the cans that are 0.011 in. thick. The values in the data set are the measured axial loads of cans, and the top lids are pressed into place with pressures that vary between 158 lb and 165 lb.

Analyzing the Results

Based on the given process data, should the company take any corrective action? Write a report summarizing your conclusions. Address not only the issue of statistical stability, but also the ability of the cans to withstand the pressures applied when the top lids are pressed into place. Also compare the behavior of the 0.0111-in. cans to the behavior of the 0.0109-in cans and recommend which thickness should be used.

Exercise 9 (For informational purposes)

In each day of production, seven aluminum cans with thickness 0.0109 in. were randomly selected and the axial loads were measured. The ranges for the different days are listed below. Construct an R chart and determine whether the process variation is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of statistically stable variation:

Exercise 10 (For informational purposes)

\(\bar{X}\) -Chart. In each production, seven aluminum cans with thickness 0.0109 in. were randomly selected and the axial loads were measured. The means for the difference days are listed below. Construct an \(\bar{X}\) chart and determine whether the process mean is within statistical control. If it is not, identify which of the three out-of-control criteria lead to rejection of the statistically stable variation.

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Solution: The downloadable solution consists of 12 pages, 877 words and 10 charts.
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