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

###### Question:

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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