The yields from an ethanol-water distillation column have a standard deviation of 1%. Specifications call for a target yield of 93%. Management wishes to detect any decrease in the true mean yield.
A. A random sample of 8 produced the following yields. Make a hypothesis test to determine whether the true mean yield has decreased. Use a 0.01 significance level.
0.90,0.93,0.95,0.86,0.90,0.87,0.93,0.92
B. Determine the p-value associated with the test in part A.
C. Make a 99% confidence interval
D. Find out the power of this test to detect a change in the true mean yield to 92.5%
E. Find out the sample size required to achieve a power of 0.95 when the true mean yield is 92.5%