Power of Population Proportion Tests (Large Samples) In Section 9.4 we developed hypothesis tests and decision rules for testing if the popula- tion proportion had certain values. Using methods similar to those in the previous section, we can also develop the probability of Type II error for proportion tests. The probability, B, of making a Type II error for any given population proportion P, included in H, is found as follows: 1. From the test decision rule, find the range of values of the sample proportion leading to failure to reject the null hypothesis. 2. Using the value P, for the population proportion--where P, is included in the al- ternative hypothesis-find the probability that the sample proportion will be in the 9.5 Assessing the Power of a Test 351 22 nonrejection region determined in step 1 for samples of n observations when the population proportion is P,- We demonstrate this procedure in the following example, Example 9.6 Forecasts of Corporate Earnings for Electronic Investors Inc. (Power and Type II Error) The president of Electronic Investors, Inc., has asked you to prepare an analysis of the forecasts of corporate earnings per share that were made by a group of financial ana- lysts. These researchers were equally interested in the proportion of forecasts that ex- ceeded the actual level of earnings and the proportion of forecasts that were less than the actual level of earnings