Question

Refer again to Exercise 10.8 on Page 427, where each pair of graphs shows the distribution of a variable on two populations. Suppose that, in each case you want to perform a small test hypothesis test based on independent simple random samples to compare the means of the two populations. In each case, decide which case, if any, of the following test is preferrable: the pooled t-test, or the Mann Whitney test. Explain your anser.

Short answer

From figure 10.8 (a), the two standard deviations are similar and the two distribution are normal.

Hence the assumption for pooled t-test is met. Hence the pooled t-test is preferrable.

From figure 10.8 (b), the two standard deviations are not similar and the two distribution are normal.

Hence the assumption for non pooled t-test is met. Hence the non pooled t-test is preferrable.

From figure 10.8 (c), the two standard deviations are not normal with same shape.

Hence the assumption for Mann Whitney test is met. Hence the Mann Whitney test is preferrable.

Step-by-step solution

Part (a) Step 1. Given Information.

Each pair of graphs shows the distribution of a variable on two populations.

Part (b) Step 2. Assumption for pooled t-test.

1. The selected sample should be a simple random sample from two populations.

2. The samples are independent of one another.

3. Population is approximately normal.

4. Equal population standard deviations.

From figure 10.8 (a), the two standard deviations are similar and the two distribution are normal.

Hence the assumption for pooled t-test is met. Hence the pooled t-test is preferrable.

Step 3. Assumption for Mann Whitney test.

1. The samples are independent of one another with same shape.

2. Population does not follow normal.

3. Sample size is not large.

From figure 10.8 (c), the two standard deviations are not normal with same shape.

Hence the assumption for Mann Whitney test is met. Hence the Mann Whitney test is preferrable.

Step 4. Assumption for non-pooled t-test.

1. The selected sample should be a simple random sample from two populations.

2. The samples are independent of one another.

3. Population is approximately normal.

4. Sample size is not large.

From figure 10.8 (b), the two standard deviations are not similar and the two distribution are normal.

Hence the assumption for non pooled t-test is met. Hence the non pooled t-test is preferrable.