Chapter 9: Introduction to Hypothesis Testing

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394 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING The t-test statistic is x t 64. 2 64 111 . s 072 . n Step 6 Reach a decision. Because t 1.11 is not less than 2.1315 and not greater than 2.1315, we do not reject the null hypothesis. Step 7 Draw a conclusion. Based on these sample data, the company does not have sufficient evidence to conclude that the filling machine is out of adjustment. 16 EXAMPLE 9-8 Testing the Hypothesis for , Unknown TRY PROBLEM 9.16 The Qwest Company The Qwest Company operates service centers in various cities where customers can call to get answers to questions about their bills. Previous studies indicate that the distribution of time required for each call is normally distributed, with a mean equal to 540 seconds. Company officials have selected a random sample of 16 calls and wish to determine whether the mean call time is now fewer than 540 seconds after a training program given to call center employees. Step 1 Specify the population parameter of interest. The mean call time is the population parameter of interest. Step 2 Formulate the null and alternative hypotheses. The null and alternative hypotheses are H 0 : μ 540 seconds (status quo) H A : μ 540 seconds Step 3 Specify the significance level. The test will be conducted at the 0.01 level of significance. Thus, α 0.01. Step 4 Construct the rejection region. Because this is a one-tailed test and the rejection region is in the lower tail, the critical value from the t-distribution with 16 1 15 degrees of freedom is t t 0.01 2.6025. Step 5 Compute the test statistic. The sample mean for the random sample of 16 calls is seconds, and the sample standard deviation is s Step 6 Reach a decision. Because t 2.67 2.6025, the null hypothesis is rejected. n 45 seconds. Assuming that the population distribution is approximately normal, the test statistic is x t 510 540 267 . s 45 Step 7 Draw a conclusion. There is sufficient evidence to conclude that the mean call time for service calls has been reduced below 540 seconds. 16 ∑( x x) 2 n 1 x∑ x/ n510
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 395 Business Application Excel and Minitab Tutorial FRANKLIN TIRE AND RUBBER COMPANY The Franklin Tire and Rubber Company recently conducted a test on a new tire design to determine whether the company could make the claim that the mean tire mileage would exceed 60,000 miles. The test was conducted in Alaska. A simple random sample of 100 tires was tested, and the number of miles each tire lasted until it no longer met the federal government minimum tread thickness was recorded. The data (shown in thousands of dollars) are in the CD-ROM file called Franklin. The null and alternative hypotheses to be tested are H 0 : 60 H A : 60 (research hypothesis) 0.05 Excel does not have a special procedure for testing hypotheses for single population means. However, the Excel add-ins software called PHStat on the CD-ROM that accompanies this text has the necessary hypothesis-testing tools. Figure 9.7a and Figure 9.7b show the Excel PHStat and the Minitab outputs. 5 We denote the critical value of an upper- or lower-tail test with a significance level of as t or t . The critical value for 0.05 and 99 degrees of freedom is t 1.6604. Using the critical value approach, the decision rule is If the t test statistic > 1.6604 t α , reject H 0 ; otherwise, do not reject H 0 . FIGURE 9.7A Excel 2007 (PHStat) Output for Franklin Tire Hypothesis Test Results Because t = 0.361 < 1.6604, do not reject H 0 . Because p-value = 0.3592 > alpha = 0.05, do not reject H 0 . Test Statistic p-value Excel 2007 (PHStat) Instructions: 1. Open file Franklin.xls. 2. Click on PHStat tab. 3. Select One Sample Test, t-test for Mean, Sigma Unknown. 4. Enter Hypothesized Mean. 5. Check “Sample Statistics Unknown”. 6. Check One-Tailed Test. 5 This test can be done in Excel without the benefit of the PHStat add-ins by using Excel equations. Please refer to the Excel tutorial on your CD-ROM for the specifics.
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Chapter 9: Introduction to Hypothesis Testing

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