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7. A printer company claims that the mean warm-up time of a certain brand of printer is at most 10 seconds. An engineer of another company is conducting a statistical test to show this is an underestimate, and the mean warm-up time is more than 10 seconds. a) State the testing hypothesis. b) The test yielded a p-value of 0.035. What would be the decision of the test if α = 0.05? c) Suppose a further study establishes that the true mean warm-up time is 9 seconds. Did the engineer make the correct decision in part (b)? If not, what type of error did he/she make? 8. The incubation period of respiratory infection is known to have a normal distribution with a mean of 8 days and a standard deviation of 3 days. Suppose a group of researchers claimed that the true mean incubation period is shorter than 8 days. A test is conducted using a random sample of 20 patients. a) Formulate hypotheses for this test. b) Consider a rejection region (X ≤6}. Suppose the test failed to reject Ho. If the true mean incubation period is 5 days, what is the Type II error probability of the test using σ =3?

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