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 7.47

7.47 Understanding concepts.

For each of the following, answer the question and give a short explanation of your reasoning.

  1. A 95% confidence interval for the difference between two means is reported as (0.3, 0.7). What can you conclude about the results of a level significance test of the null hypothesis that the population means are equal versus the two-sided alternative?
  2. Will larger samples generally give a larger or smaller margin of error for the difference between two sample means?

7.47

(a) Because 0 is not in the interval, we can reject the null hypothesis; the data support a significant difference between the two means. (b) Generally, a larger sample will result in a smaller margin of error.