Section 9.4 Hypothesis Tests for Proportions 453 Step 4: Determine whether to reject H0. Because this is a right-tailed test, we reject H0 if z ≥ 1.645. Because 0.80 < 1.645, we do not reject H0. See Figure 9.17. Critical region: Area = 0.05 1.645 z = 0.80 Critical value Figure 9.17 Step 5: State a conclusion. There is not enough evidence to conclude that the company president is correct in his belief that the proportion of employees who are satisfied with their jobs is greater than 0.5. The proportion may be equal to 0.5. Check Your Understanding 4. A Gallup poll taken in December 2009 sampled 1000 adults in the United States. Of these people, 770 said they enjoyed situations in which they competed with other people. Can you conclude that less than 80% of U.S. adults like to compete? Use the critical value method with significance level �� = 0.05. a. State the null and alternate hypotheses. H0 : p = 0.8, H1: p < 0.8 b. Compute the test statistic. −2.37 c. Find the critical value. −1.645 d. State a conclusion. Answers are on page 458. USING TECHNOLOGY We use Example 9.20 to illustrate the technology steps. TI-84 PLUS Testing a hypothesis about a proportion Step 1. Press STAT and highlight the TESTS menu. Step 2. Select 1–PropZTest and press ENTER (Figure A). The 1–PropZTest menu appears. Step 3. Enter the values of p0, x, and n. For Example 9.20, we use p0 = 0.5, x = 54, and n = 100. Step 4. Select the form of the alternate hypothesis. For Example 9.20, the alternate hypothesis has the form >p0 (Figure B). Step 5. Highlight Calculate and press ENTER (Figure C). Figure A Figure B Figure C
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