Tukey's Quick Test. In this exercise, we examine an alternative method, conceived by the late Professor John Tukey, for performing a two-tailed hypothesis test for two population means based on independent random samples. To apply this procedure, one of the samples must contain the largest observation (high group) and the other sample must contain the smallest observation (low group). Here are the steps for performing Tukey's quick test.
Step 1 Count the number of observations in the high group that are greater than or equal to the largest observation in the low group. Count ties as 1/2.
Step 2 Count the number of observations in the low group that are less than or equal to the smallest observation in the high group. Count ties as 1/2.
Step 3 Add the two counts obtained in Steps 1 and 2, and denote the sum c.
Step 4 Reject the null hypothesis at the 5% significance level if and only if c ≥ 7; reject it at the 1% significance level if and only if c ≥ 10; and reject it at the 0.1% significance level if and only if c ≥ 13.
a. Can Tukey's quick test be applied to Exercise 10.42 on page 407? Explain your answer.
b. If your answer to part (a) was yes, apply Tukey's quick test and compare your result to that found in Exercise 10.42, where a t-test was used.
c. Can Tukey's quick test be applied to Exercise 10.76? Explain your answer.
d. If your answer to part (c) was yes, apply Tukey's quick test and compare your result to that found in Exercise 10.76, where a t-test was used.
For more details about Tukey's quick test, see J. Tukey, "A Quick, Compact, Two-Sample Test to Duckworth's Specifications" (Technometrics, Vol. 1, No. 1, pp. 31-48).