A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 12 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis Ho: H= 12 against H₁:μ< 12, using a random sample of 4 specimens. Round your answers to 4 decimal places. (a) What is the type I error probability if the critical region is defined as I < 11.5 kilograms? The type 1 error probability is (b) Find for the case where the true mean elongation is 11.22 kilograms. B = A (c) Find for the case where the true mean is 11.5 kilograms. p=

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