Question

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 I 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 $\frac{1}{2}$.

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 $\frac{1}{2}$.

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 the0.1% significance level if and only
ifc≥13.
a. Can Tukey's quick test be applied to Exercise 10.48 on page 416? 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 10.48, where a t-test was used.
c. Can Tukey's quick test be applied to Exercise 10.74? 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 10.74, where a t-test was used.

Short answer

(a) No, Turkey's quick test is not applicable to Exercise 10.42 because both the higher and lower value occurs in the "South Household" data.

(b) Turkey's quick test cannot be applied. Therefore, Turkey's quick test cannot be compared with the result found in Exercise 10.42.

(c)Yes, Turkey's quick test is applied to Exercise 10.86, because the lowest value appears in the group migraatory and the highest value appears in the group non-migratory.

(d)So the value of c is greater than 10 so the null hypotheiss is rejected at 1% level. Hence the result obtained in both t-pooled test and Turkey's quick test are similar.

Step-by-step solution

Part (a) Step 1. GIven Information.  

About Turkey's quick test and using it for above mentioned exercises.

Part (a) Step 2. Turkey's test.

No, Turkey's quick test is not applicable to Exercise 10.48 because both the higher and lower value occurs in the "South Household" data.

Part (b) Step 1. Explanation.

Turkey's quick test cannot be applied. Therefore, Turkey's quick test cannot be compared with the result found in Exercise 10.48.

Part (c) Step 1. Turkey's test to exercise 10.86.

Yes, Turkey's quick test is applied to Exercise 10.86, because the lowest value appears in the group migraatory and the highest value appears in the group non-migratory.

Part (d) Step 1. Comparing the result.

From the given data set, the higher value in the group "migratory" is 84.95.

There are seven values that are lesser than the higher vaue in the group "non-migratory".

From the given data set, the lower value in the group "non-migratory" is 82.1.

There are six values that are lower than the lower value in the group "non-migratory".

So,

$$\begin{gathered} c=7+6+\frac{1}{2} \\ =13.5 \end{gathered}$$

So the value of c is greater than 10 so the null hypotheiss is rejected at 1% level. Hence the result obtained in both t-pooled test and Turkey's quick test are similar.