Chapter 9: Introduction to Hypothesis Testing

More documents

Recommendations

Info

396 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING FIGURE 9.7B Minitab Output for Franklin Tire Hypothesis Test Results p-value Test Statistic Minitab Instructions: 1. Open file: Franklin.MTW. 2. Choose Stat Basic Statistics 1-sample t. 3. In Samples in columns, enter data column. 4. Select Perform hypothesis test and enter hypothesized mean. 5. Select Options, in Confidence level insert confidence level. 6. In Alternative, select hypothesis direction. 7. Click OK. The sample mean, based on a sample of 100 tires is x 60.17 (60,170 miles), and the sample standard deviation is s 4.701 (4,701 miles). The t test statistics shown in Figure 9.7a and 9.7b are computed as follows: Because t 0.3616 < t 0.05 1.6604, do not reject the null hypothesis. Thus, based upon the sample data, the evidence is insufficient to conclude that the new tires have an average life exceeding 60,000 miles. Based on this test, the company would not be justified in making the claim. Franklin managers could also use the p-value approach to test the null hypothesis because the output shown in Figures 9.7a and 9.7b provides the p-value. In this case, the p-value 0.3592. The decision rule for a test is Because x t 60. 17 60 0. 3616 s 4. 701 n 100 If p-value α reject H 0 ; otherwise, do not reject H 0 . p-value 0.3592 0.05 we do not reject the null hypothesis. This is the same conclusion we reached using the t test statistic approach. This section has introduced the basic concepts of hypothesis testing. There are several ways to test a null hypothesis. Each method will yield the same result; however, computer software such as Minitab and Excel show the p-values automatically. Therefore, decision makers increasingly use the p-value approach.
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 397 9-1: Exercises Skill Development 9-1. Determine the appropriate critical value(s) for each of the following tests concerning the population mean: a. upper-tailed test: 0.025; n 25; 3.0 b. lower-tailed test: 0.05; n 30; s 9.0 c. two-tailed test: 0.02; n 51; s 6.5 d. two-tailed test: 0.10; n 36; 3.8 9-2. For the following hypothesis test: H 0 : 200 H A : 200 0.01 with n 64, σ 9, and x 196.5, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-3. For the following hypothesis test: H 0 : 23 H A : 23 0.025 with n 25, s 8, and x 20, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-4. For the following hypothesis test: H 0 : 45 H A : 45 0.02 with n 80, 9, and x 47.1, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the appropriate p-value. d. the conclusion. 9-5. For the following hypothesis test: H 0 : 60.5 H A : 60.5 0.05 with n 15, s 7.5, and x 62.2, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-6. For the following hypothesis: H 0 : 70 H A : 70 with n 20, x 71.2, s 6.9, and 0.1, state a. the decision rule in terms of the critical value of the test statistic. b. the calculated value of the test statistic. c. the conclusion. 9-7. For each of the following z-test statistics, compute the p-value assuming that the hypothesis test is a one-tailed test: a. z 1.34 b. z 2.09 c. z 1.55 9-8. For each of the following pairs of hypotheses, determine whether each pair represents valid hypotheses for a hypothesis test. Explain reasons for any pair that is indicated to be invalid. a. H 0 : 15, H A : 15 b. H 0 : 20, H A : 20 c. H 0 : 30, H A : 30 d. H 0 : 40, H A : 40 e. H 0 : x 45, H A : x 45 f. H 0 : 50, H A : 55 9-9. A sample taken from a population yields a sample mean of 58.4. Calculate the p-value for each of the following circumstances: a. H A : 58, n 16, 0.8 b. H A : 45, n 41, s 35.407 c. H A : 45, n 41, 35.407 d. H A : 69; data: 60.1, 54.3, 57.1, 53.1, 67.4 9-10. Provide the relevant critical value for each of the following circumstances: a. H A : 13, n 15, 10.3, 0.05 b. H A : 21, n 23, s 35.40, 0.02 c. H A : 35, n 41, 35.407, 0.01 d. H A : 49; data: 12.5, 15.8, 44.3, 22.6, 18.4; 0.10 e. H A : 15, n 27, 12.4 9-11. For each of the following scenarios, indicate which type of statistical error could have been committed or, alternatively, that no statistical error was made. When warranted, provide a definition for the indicated statistical error. a. Unknown to the statistical analyst, the null hypothesis is actually true. b. The statistical analyst fails to reject the null hypothesis. c. The statistical analyst rejects the null hypothesis. d. Unknown to the statistical analyst, the null hypothesis is actually true and the analyst fails to reject the null hypothesis. e. Unknown to the statistical analyst, the null hypothesis is actually false. f. Unknown to the statistical analyst, the null hypothesis is actually false and the analyst rejects the null hypothesis.
Page 1 and 2: Chapter NINE Introduction to Hypoth
Page 3 and 4: CHAPTER 9 • INTRODUCTION TO HYPOT
Page 21: CHAPTER 9 • INTRODUCTION TO HYPOT

Chapter 9: Introduction to Hypothesis Testing

Create successful ePaper yourself

Delete template?

Save as template?