Chapter 9: Introduction to Hypothesis Testing

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420 CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING TABLE 9.1 Statistical Inference Tools—One Sample Situations Statistic Confidence Interval Population Mean Population Proportion x x x ∑ p n n known: p( 1 p) x z pz n n unknown: s x t n Hypotheses Example Example Test Statistic H 0 : 200 H 0 : 0.60 H A : 200 H A : 0.60 known: p z x z ( 1) n n unknown: x t s n have little or no idea of the value of a population parameter and are primarily interested in determining these values. On the other hand, hypothesis testing is used when a claim about a population parameter needs to be tested. Estimation and hypothesis testing are the central components of statistical inference and will be used throughout the remaining chapters of this text. Figure 9.13 on the previous page is a flow diagram that should help you determine which hypothesistesting procedure to use in various situations. Note: Figure 9.13 assumes a right-tailed hypothesis test. Table 9.1 provides a matrix format to help you determine which statistical tools to apply in specific situations. Equations x for Hypothesis Tests, Known x z n (9.1) z-Test Statistic for Hypothesis Tests for , Known t-Test Statistic for Hypothesis Tests for , Unknown z-Test Statistic for Proportions Power z x z n x t s n p (1 ) n (9.2) (9.3) (9.4) Power 1 β (9.5) Key Terms Alternative hypothesis 376 Critical value 382 Null hypothesis 376 One-tailed test 389 p-value 387 Power 414 Power curve 415 Research hypothesis 377 Significance level 381 Two-tailed test 389 Test statistic 384 Type I error 380 Type II error 380
CHAPTER 9 • INTRODUCTION TO HYPOTHESIS TESTING 421 Chapter Exercises Conceptual Questions 9-67. Discuss the two types of statistical errors that can occur when a hypothesis is tested. Illustrate what you mean by using a business example for each. 9-68. Discuss the issues a decision maker should consider when determining the significance level to use in a hypothesis test. 9-69. What is meant by the term critical value in a hypothesis-testing situation? Illustrate what you mean with a business example. 9-70. Discuss why it is necessary to use an estimate of the standard error for a confidence interval and not for a hypothesis test concerning a population proportion. 9-71. What is the maximum probability of committing a Type I error called? How is this probability determined? Discuss. 9-72. Recall that the power of the test is the probability the null hypothesis is rejected when H 0 is false. Explain whether power is definable if the given parameter is the value specified in the null hypothesis. 9-73. Examine the test statistic used in testing a population proportion. Why is it impossible to test the hypothesis that the population proportion equals zero using such a test statistic? Try to determine a way that such a test could be conducted. 9-74. The Oasis Chemical Company develops and manufactures pharmaceutical drugs for distribution and sale in the United States. The pharmaceutical business can be very lucrative when useful and safe drugs are introduced into the market. Whenever the Oasis research lab considers putting a drug into production, the company must actually establish the following sets of null and alternative hypotheses: Set 1 Set 2 H 0 : The drug is safe. H A : The drug is not safe. H 0 : The drug is effective. H A : The drug is not effective. Take each set of hypotheses separately. a. Discuss the considerations that should be made in establishing alpha and beta. b. For each set of hypotheses, describe what circumstances would suggest that a Type I error would be of more concern. c. For each set of hypotheses, describe what circumstances would suggest that a Type II error would be of more concern. 9-75. For each of the following scenarios, indicate which test statistic would be used or which test could not be conducted using the materials from this chapter: a. Testing a mean when is known and the population sampled from has a normal distribution. b. Testing a mean when is unknown and the population sampled from has a normal distribution. c. Testing a proportion in which n 12 and n(1 − ) 4. d. Testing a mean when s is obtained from a small sample and the population sampled from has a skewed distribution. 9-76. In a hypothesis test, indicate the type of statistical error that can be made if a. the null hypothesis is rejected. b. the null hypothesis is not rejected. c. the null hypothesis is true. d. the null hypothesis is not true. 9-77. While conducting a hypothesis test, indicate the effect on a. when is decreased while the sample size remains constant. b. when is held constant and the sample size is increased. c. the power when is held constant and the sample size is increased. d. the power when is decreased and the sample size is held constant. Business Applications 9-78. Peterson Automotive is the local dealership selling Honda automobiles. It recently stated in an advertisement that Honda owners average more than 85,000 miles before trading in or selling their Honda. To test this, an independent agency selected a simple random sample of 80 Honda owners who have either traded or sold their Honda and determined the number of miles on the car when the owner parted with the car. They plan to test Peterson’s claim at the alpha 0.05 level. a. State the appropriate null and alternative hypotheses. b. If the sample mean is 86,200 miles and the sample standard deviation is 12,000 miles, what conclusion should be reached about the claim? 9-79. The Ohio State Tax Commission attempts to set up payroll-tax withholding tables such that by the end of the year, an employee’s income tax withholding is about $100 below his actual income tax owed to the state. The commission director claims that when all the Ohio tax returns are in, the average additional payment will be less than $100.
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Chapter 9: Introduction to Hypothesis Testing

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