Precision Instruments Assume the means of two populations are

Precision Instruments Assume (as in the case of measurements produced by two well-calibrated measuring instruments) the means of two populations are equal. Use the Wilcoxon rank sum statistic for testing hypotheses concerning the population variances as follows:

a. Rank the combined sample.

b. Number the ranked observations “from the outside in”; that is, number the smallest observation 1, the largest 2, the next-to-smallest 3, the next-to-largest 4, and so on. This sequence of numbers induces an ordering on the symbols A (population A items) and B (population B items).If  one would expect to find a preponderance of A’s near the first of the sequences, and thus a relatively small “sum of ranks” for the A observations.

c. Given the measurements in the table produced by well-calibrated precision instruments A and B, test at near the a = .05 level to determine whether the more expensive instrument B is more precise than A. (Note that this implies a one-tailed test.) Use the Wilcoxon rank sum test statistic.

Instrument A	Instrument B
1060.21	1060.24
1060.34	1060.28
1060.27	1060.32
1060.36	1060.30
1060.40

d. Test using the equality of variance F-test.