7.91 Revisiting the small-sample example. Refer to Example 7.16 (page 444). This is a case where the sample sizes are quite small. With only five observations per group, we have very little information to make a judgment about whether the population standard deviations are equal. The potential gain from pooling is large when the sample sizes are small. Assume that we will perform a two-sided test using the 5% significance level.
(a) Find the critical value for the unpooled t test statistic that does not assume equal variances. Use the minimum of and for the degrees of freedom.
(b) Find the critical value for the pooled t test statistic.
(c) How does comparing these critical values show an advantage of the pooled test?