14.80 Pooling variances, continued.

Refer to Exercise 14.43 (page 750). Based on our rule of thumb (page 720), we consider it reasonable to use the assumption of equal standard deviations in our analysis. However, when sample sizes vary substantially, we need to use caution. As demonstrated in Exercise 14.43, the pooled standard deviation is closer to the standard deviation of the third group than any of the other three standard deviations. Assuming these sample standard deviations are close to the population standard deviations, explain the impact of using the pooled standard deviation on the coverage of the simultaneous confidence intervals between means. In particular, would you expect the coverage of the interval for the difference between the first and second group to be larger or smaller than ? Explain your answer.