Discuss the below:
Q: The Crown Bottling Company has just installed a new bottling process that will fill 16-ounce bottles of the popular Crown Classic Cola soft drink. Both overfilling and underfilling bottles are undesirable. The company would like to know if the average fill volume is different than 16 ounces. They take a sample of 15 bottles, measure the contents, and calculate a sample average of 16.02 and a sample standard deviation of 0.10.
a) What is the appropriate null and alternate hypothesis to determine if the fill process requires adjustment?
b) Test the hypothesis using ? = 0.03. Show explicitly the critical value, rejection region, and how you calculated the test statistic. Explicitly state whether or not you reject the null hypothesis and why.
c) Repeat the hypothesis test using the Z distribution instead of the t distribution to find the critical value. Does your conclusion change?