Section 9.5 Summary

1. The test statistic used for the test for the proportion is

   where is the observed sample proportion of successes, is the value of hypothesized in , , and is the sample size. represents the number of standard deviations the sample proportion lies above or below the hypothesized proportion . Extreme values of will be associated with extreme values of . The test for the proportion may be performed using either the -value method or the critical-value method. For the critical-value method, we compare the values of and . If falls in the critical region, we reject .

2. For the -value method, we reject if the .
3. We can use a single confidence interval for to help us perform any number of two-tailed hypothesis tests about with level of significance .