Section 9.4 Hypothesis Tests for Proportions 451 a. What are the null and alternate hypotheses? H0 : p = 0.6, H1: p < 0.6 b. What is the sample size? 150 c. What is the value of ̂p? 0.48 d. What is the value of the test statistic? −3.00 e. Do you reject H0 at the 0.05 level? Yes f. Do you reject H0 at the 0.01 level? Yes 3. The following display from a TI-84 Plus calculator presents the results of a hypothesis test. a. What are the null and alternate hypotheses? H0 : p = 0.75, H1: p > 0.75 b. What is the sample size? 1225 c. What is the value of ̂p? 0.7559183673 d. What is the value of the test statistic? 0.4783759373 e. Do you reject H0 at the 0.05 level? No f. Do you reject H0 at the 0.01 level? No Answers are on page 458. Objective 2 Test a hypothesis about a proportion using the critical value method Testing Hypotheses for a Proportion Using the Critical Value Method To use the critical value method, compute the test statistic as before. Because the test statistic is a z-score, critical values can be found in Table A.2, in the last line of Table A.3, or with technology. The assumptions for the critical value method are the same as for the P-value method. Assumptions for Performing a Hypothesis Test for a Population Proportion 1. We have a simple random sample. 2. The population is at least 20 times as large as the sample. 3. The items in the population are divided into two categories. 4. The values np0 and n(1 − p0) are both at least 10. Following are the steps for the critical value method. Performing a Hypothesis Test for a Proportion Using the Critical Value Method Check to be sure the assumptions are satisfied. If they are, then proceed with the following steps: Step 1: State the null and alternate hypotheses. The null hypothesis will have the form H0 : p = p0. The alternate hypothesis will be p < p0, p > p0, or p ≠ p0. Step 2: Choose a significance level �� and find the critical value or values. Step 3: Compute the test statistic z = ̂p − p0 √ p0(1 − p0) n .
navidi_monk_elementary_statistics_2e_ch7-9
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