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SAT , 22.03.2022 17:37

Every day, a quality control inspector of high-quality dishes selects a random sample of 100 dishes and carefully inspects each dish for defects. If the inspector finds convincing evidence that the true proportion of defective dishes is more than 0.10, then the manufacturing process will be shut down for a complete inspection of the system (a) Define the parameter and specify the hypotheses. (b) Describe the sampling distribution of the sample proportion of defective dishes assuming that the true proportion of defective dishes is 0.10. Sketch the sampling distribution. (c) Using a significance level of 10%. what values of p would provide sufficient evidence to reject the null hypothesis? Identify this rejection region on your sampling distribution from part (b). (d) Recognizing that the sample mean changus from sample-to-sample and that the null hypothesis may or may not be true describe the four outcomes for the conclusion of this inference procedure. Then describe a consequence for each of these outcomes. Nu vypothesis (M) Table of error types Tre False Outcome 1 Outcome Retet pote) true positive 1- Decision about us hypothesis in) Outcome 2 Face Outcoma 4 TV DOO -1.0 probaby- (e) Suppose that the true proportion of defective dishes really is 0.16. Describe the sampling distribution of the sample proportion assuming the true proportion is 0.16. Sketch this sampling distribution below your sampling distribution from part (b). (1) Identify the four outcomes on your two sampling distributions in part (e). () Find the probabilities of the four outcomes. What do we call these probabilities? (h) List two ways to increase the power of this test

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