Question: Suppose that the sample sizes n1 and n2 are equal

Suppose that the sample sizes, n1 and n2, are equal for independent simple random samples from two populations.
a. Show that the values of the pooled and nonpooled t-statistics will be identical. (Hint: Refer to Exercise 10.55 on page 408.)
b. Explain why part (a) does not imply that the two t-tests are equivalent (i.e., will necessarily lead to the same conclusion) when the sample sizes are equal.

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