You work for a popular pizzeria in suburbs that has recently considered providing a guarantee on delivery times (e.g. "Guaranteed delivery within 50 minutes, or your pizza is free!"). However, you are quite concerned about just how many pizzas you will be giving away for free under such a policy. You shift manager claims that delivery times are uniformly distributed between 30 minutes and an hour, but you are not so sure about this. Luckily, you have been recording the actual delivery times for the past several years and have assembled a dataset with 30 observed actual delivery times (DeliveryTimes.xlsx).

e. If you were to implement a policy of only charging for pizzas that are delivered in under 50 minutes, would it matter which distribution was the correct one? Why

or why not? (Note: you do not need to compute anything here, just answer the question from an intuitive standpoint).

f. Again using the information from part a), construct a 95% confidence interval for the population mean. How does this compare to the 95% interval you constructed in part c (for the Normal case)? If it is different, what is the reason for this?

g. Would the confidence interval you constructed in part f) change if you assumed the population distribution was uniform instead of Normal? Why or why not?

h. Using the information from part a), test the null hypothesis that the population average delivery time is 50 minutes against the two-sided alternative hypothesis

that it is not 50 minutes at both the 1% and 5% levels. What do you conclude?