A coffee shop sells on the average 320 cups of coffee per day, with a standard deviation of 40. After advertising, they find that on 7 days they sell an average of 350 cups.
(a) Has advertising left their business unchanged? Calculate the prob-value.
(b) If the owner of the coffee shop specifies that the type I error of the test (significance level) is to be 5 %, do you reject the hypothesis that business is unchanged?
(c) What assumptions have you made implicitly in parts (a) and (b)? Under what conditions are they questionable?
(d) If coffee sales can be observed for 25 days, what would the average sales have to be in order to justify a statement that business had improved, at the 5 % significance level?