Ch09 - 9 1 Chapter 9 Hypothesis Tests Learning Objectives 1...

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Unformatted text preview: 9 - 1 Chapter 9 Hypothesis Tests Learning Objectives 1. Learn how to formulate and test hypotheses about a population mean and/or a population proportion. 2. Understand the types of errors possible when conducting a hypothesis test. 3. Be able to determine the probability of making various errors in hypothesis tests. 4. Know how to compute and interpret p-values. 5. Be able to use critical values to draw hypothesis testing conclusions. 6. Be able to determine the size of a simple random sample necessary to keep the probability of hypothesis testing errors within acceptable limits. 7. Know the definition of the following terms: null hypothesis two-tailed test alternative hypothesis p-value Type I error level of significance Type II error critical value one-tailed test power curve Chapter 9 9 - 2 Solutions: 1. a. H : µ ≤ 600 Manager’s claim. H a : µ > 600 b. We are not able to conclude that the manager’s claim is wrong. c. The manager’s claim can be rejected. We can conclude that µ > 600. 2. a. H : µ ≤ 14 H a : µ > 14 Research hypothesis b. There is no statistical evidence that the new bonus plan increases sales volume. c. The research hypothesis that µ > 14 is supported. We can conclude that the new bonus plan increases the mean sales volume. 3. a. H : µ = 32 Specified filling weight H a : µ ≠ 32 Overfilling or underfilling exists b. There is no evidence that the production line is not operating properly. Allow the production process to continue. c. Conclude µ ≠ 32 and that overfilling or underfilling exists. Shut down and adjust the production line. 4. a. H : µ ≥ 220 H a : µ < 220 Research hypothesis to see if mean cost is less than $220. b. We are unable to conclude that the new method reduces costs. c. Conclude µ < 220. Consider implementing the new method based on the conclusion that it lowers the mean cost per hour. 5. a. The Type I error is rejecting H when it is true. In this case, this error occurs if the researcher concludes that the mean newspaper-reading time for individuals in management positions is greater than the national average of 8.6 minutes when in fact it is not. b. The Type II error is accepting H when it is false. In this case, this error occurs if the researcher concludes that the mean newspaper-reading time for individuals in management positions is less than or equal to the national average of 8.6 minutes when in fact it is greater than 8.6 minutes. 6. a. H : µ ≤ 1 The label claim or assumption. H a : µ > 1 b. Claiming µ > 1 when it is not. This is the error of rejecting the product’s claim when the claim is true. Hypothesis Testing 9 - 3 c. Concluding µ ≤ 1 when it is not. In this case, we miss the fact that the product is not meeting its label specification....
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Ch09 - 9 1 Chapter 9 Hypothesis Tests Learning Objectives 1...

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