In: Statistics and Probability
A textile fiber manufacturer is investigating a new drapery yarn, which the company claims has a mean thread elongation of 15 kilograms with a standard deviation of 0.5 kilograms. The company wishes to test the hypothesis H_0: mu = 15 against H_1: mu > 15 using a random sample of 4 specimens. Suppose also that the critical region (rejection region) is defined as (sample mean) X_bar > 15.41 kilograms. Calculate the beta value for the case where the true mean elongation is 15.7 kilograms