A quality control supervisor in a Coca-Cola cannery knows that the exact amount each can contains will vary, since there are certain uncontrollable factors that affect the amount of fill. The mean fill per can is important, but equally important is the variance of the fill. If σ2 is large, some cans will contain too little and others too much. suppose regulatory agencies specify that the standard deviation of the amount of fill in 16-ounce cans of Coca-Cola should be less than 0.1 ounce. To determine whether the process in meeting this specification, the supervisor randomly selects 10 cans and weighs the contents of each. The results are given below:

Fill Weights (ounces) of 10 Cans of Coca-Cola
16.00 15.95 16.10 16.02 15.90 16.06 16.04 16.05 16.03 16.02
Is there sufficient evidence to conclude that the true standard deviation σ of the fill measurements of 16-ounce cans is less than 0.1 ounce?
a. Test the hypothesis H0: σ = 0.1 (fill specifications are met) against Ha: σ < 0.1 (fill specifications are not met), at α = 0.05.
b. Calculate the 95% confidence interval for the population mean.
c. What minimum sample size would be required if the power of the test were to be 0.99?
d. Determine the power of the original test.