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Your company manufactures 150 mg ibuprofen tablets. You randomly sample 20 tablets and measure their mass,...

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Your company manufactures 150 mg ibuprofen tablets. You randomly sample 20 tablets and measure their mass, then calculate the

Your company manufactures 150 mg ibuprofen tablets. You randomly sample 20 tablets and measure their mass, then calculate the average mass X from this sample. You know that the standard deviation of tablet mass from your manufacturing process is o=6 mg. a. Specify a null and alternative process to determine whether or the mass of ibuprofen tablets from your process is 150 mg. b. You reject the null hypothesis Ho: u = 150 mg if the average mass of 20 tablets X falls outside the range of 150 = 2 mg. What is the type I error probability a? c. Find the value of Ax so that the type I error probability a = 0.01 or 1% if you reject the null hypothesis Ho: u = 150 mg if the average mass of 20 tablets X falls outside the range of 150 + Ax mg. d. You hope your test is powerful enough to detect a 5 mg change in the mean tablet mass u, so you specify the alternative to be Hi: u = 145 or u = 155 mg. What is the type II error probability B if you decide to reject the null hypothesis if the average mass of 20 tablets X falls outside the range of 150 = 2 mg? e. What change in mass can be detected if type II error probability B = 0.01? In other words, find Ax so that an alternative of Hi: u = 150 - Ax or u = 150 + Ax will result in a type II error probability B = 0.01 if you reject the null hypothesis when the average mass of 20 tablets & falls outside the range of 150 – 2 mg.

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