Chapter 9: Introduction to Hypothesis Testing

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402 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING The z-value for this test statistic is 0. 0150. 01 z 125 . 0. 004 As was established in Figure 9.8, the critical value is z 0.02 2.05 We reject the null hypothesis only if z z 0.02 . Because z 1.25 2.05 we don’t reject the null hypothesis. This, of course, was the same conclusion we reached when we used p as the test statistic. Both test statistics must yield the same decision. SUMMARY Testing Hypotheses About a Single Population Proportion 1. Specify the population parameter of interest. 2. Formulate the null and alternative hypotheses. 3. Specify the significance level for testing the null hypothesis. 4. Construct the rejection region. For a one-tail test, determine the critical value, z , from the standard normal distribution table or p ( 1) z n For a two-tail test, determine the critical values z (/2)L and z (/2)U from the standard normal table or p (/2)L and p (/2)U x p 5. Compute the test statistic, p or z n p( 1)/ n 6. Reach a decision by comparing z to z or p to p or by comparing the p-value to . 7. Draw a conclusion. EXAMPLE 9-9 Testing Hypotheses for a Single Population Proportion TRY PROBLEM 9.27 Season Ticket Sales A major university is considering increasing the season ticket prices for basketball games. The athletic director is concerned that some people will terminate their ticket orders if this change occurs. If more than 10% of the season ticket orders would be terminated, the AD does not want to implement the price increase. To test this, a random sample of ticket holders are surveyed and asked what they would do if the prices were increased. Step 1 Specify the population parameter of interest. The parameter of interest is the population proportion of season ticket holders who would terminate their orders. Step 2 Formulate the null and alternative hypotheses. The null and alternative hypotheses are H 0 : 0.10 H A : 0.10 (research hypothesis) Step 3 Specify the significance level. The alpha level for this test is 0.05.
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 403 Step 4 Construct the rejection region. The critical value from the standard normal table for this upper-tailed test is z z 0.05 1.645. The decision rule is If z 1.645, reject H 0 ; otherwise, do not reject. Step 5 Compute the test statistic. The random sample of n 100 season ticket holders showed that 14 would cancel their ticket orders if the price change were implemented. The sample proportion is Step 6 Reach a decision. The decision rule is x 14 p 014 . n 100 p z 014 . 010 . 133 . (1 ) 0.10(1 010 . ) n 100 If z z 0.05 , reject H 0 . Because z 1.33 1.645, do not reject H 0 . As you learned in Section 9.1, there are alternative approaches to testing a hypothesis. In addition to the z-test statistic approach, you could compute the critical value, p , and compare p 0.14 to p . The critical value is computed as follows: p p The decision rule is If p p α , reject H 0 . Because 0.14 0.149, do not reject H 0 . This is the same decision we reached using the z-test statistic approach. The hypothesis can also be tested using the p-value approach. To find the p-value for a one-tailed test, we use the calculated z-value shown previously in step 5 to be z 1.33. Then, p-value P(z 1.33) From the standard normal table, the probability associated with z 1.33 is 0.4082. Then, The decision rule is 005 . ( 1) z n 0101 . ( 010 . ) 0. 101. 645 100 p-value 0.5 0.4082 0.0918 If p-value , reject H 0 . Because p-value 0.0918 0.05, do not reject H 0 . 0. 149 All three hypothesis testing approaches provide the same decision.
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Chapter 9: Introduction to Hypothesis Testing

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