The theory of runs may also be used as an alternative to the rank- sum test of Section 16.4, that is, the test of the null hypothesis that two independent random samples come from identical continuous populations. We simply rank the data jointly, write a 1 below each value belonging to the first sample and a 2 below each value belonging to the second sample, and then test the randomness of the resulting arrangement of 1’s and 2’s. If there are too few runs, this may well be accounted for by the fact that the two samples come from populations with unequal means. With reference to the data on page 460, use this technique to test at the 0.05 level of significance whether the two samples came from identical continuous populations or whether the two populations have unequal means.

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