In exercises that call for two-sample procedures, you may use either of the two approximations for the degrees of freedom that we have discussed: the value given by your software or the smaller of and . Be sure to state clearly which approximation you have used.

Question 7.73

7.73 The advantage of pooling.

For the analysis of wheat prices in Example 7.13 (pages 385386), there are only five observations per month. When sample sizes are small, 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 very small. Assume that we will perform a two-sided test using the 5% significance level.

wheat

  1. Find the critical value for the unpooled test statistic that does not assume equal variances. Use the minimum of and for the degrees of freedom.
  2. Find the critical value for the pooled test statistic.
  3. How does comparing these critical values show an advantage of the pooled test?

7.73

(a) . (b) . (c) Because the critical value is smaller for the pooled test, it is easier to show significance than the unpooled test.