Section 6.3 Solutions

6.73

Since both p-values are less than 0.05, both sets of results are statistically significant at the 0.05 level. Yet the p-value of 0.00002 obviously contains much, much stronger evidence against the test’s null hypothesis. That is, the p-value gives us a continuum of evidence against the null hypothesis, not simply a “yes” or “no” as to significance at the 0.05 level.

6.82

a. The test statistic is and the p-value is Since the p-value is so large, the results are not significant at any reasonable significance level.

b. The test statistic is and the P-value is Since the p-value is so large, the results are not significant at any reasonable significance level.

c. The test statistic is and the P-value is Since the p-value is so small, the results are statistically significant (for any reasonable significance level) – yet they aren’t of practical significance.

6.84

a. The test statistic is and the p-value is Since the results are not statistically significant at the 0.05 level.

b. The test statistic is and the p-value is Since the results are statistically significant at the 0.05 level.

The p-values in a and b are essentially the same. Remember the p-value takes on a continuum of values and 0.05 is not a magical cutoff point.