In the famous Twix factories, Bob (the owner of the left Twix factory) believes that his brother Bill (the owner of the right Twix factory) has been saving money by reducing the weight of the right Twix bars. A random sample of 49 bars is taken from the left factory and the average weight was found to be 15.67 grams with a standard deviation of 2.34 grams. A random sample of 100 bars is also taken from the right factory and the average weight was found to be 14.92 grams with a standard deviation of 1.25 grams.

(a) Assuming a population standard deviation for both factories of 2 grams, test Bob's theory using p-values.

(b) Using the sample standard deviations given for both factories, test Bob's theory using p-values if we assume the population standard deviations are equal (but unknown) using p-values. Confirm with a printout from MINITAB.

(c) Using the sample standard deviations given for both factories, test Bob's theory using p-values if we assume the population standard deviations are NOT equal (and unknown) using p-values. Confirm with a printout from MINITAB.

(d) Explain what a TYPE I error would mean for his situation (problem context)

(e) Explain what a TYPE II error would mean for his situation (problem context)