Question: The theory of runs may also be used as an
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.
Answer to relevant QuestionsConstruct the seventh and eighth rows of Pascal’s triangle and write the binomial expansions of (x+y)6 and (x+y)7. Calculate rS for the following data representing the statistics grades, x, and psychology grades, y, of 18 students: With reference to Exercise 16.42, calculate the k = 3 pairwise rank correlation coefficients and verify that the relationship between their mean S and the coefficient of concordance (see Exercise 16.15) is given by In ...Show that (a) U1 + U2 = n1n2 for any pair of values of the corresponding random variables; (b) The random variables corresponding to U1 and U2 both take on values on the range from 0 to n1n2. The following are the numbers of defective pieces produced by a machine on 50 consecutive days: 7, 14, 17, 10, 18, 19, 23, 19, 14, 10, 12, 18, 19, 13, 24, 26, 9, 16, 19, 14, 19, 10, 15, 22, 25, 24, 20, 9, 17, 28, 29, 19, 25, ...
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