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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 pvalues. 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 twotailed test alternative hypothesis pvalue Type I error level of significance Type II error critical value onetailed 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 newspaperreading 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 newspaperreading 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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 Spring '08
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 Statistical hypothesis testing, β

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