The yield of a chemical procedure is being studied. From previous experience with this procedure the standard deviation of yield is known to be 2.9. The past five days of plant operation have resulted in the following yields (given in percentages): 91.6, 88.75, 90.8, 89.95 and 91.3%.
A) Test the hypothesis that the mean yield is not equal to 90%. Employ alpha = .01. Determine the numerical value of the test statistic? Answer to two decimal places.
B) If the true population mean yield is 92%, what is beta, the probability of the Type II error? Answer to three decimal places. (Remember that this is a 2-sided test and that alpha is .01.)