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## Statistic Quiz Questions & Excel Worksheet

### Question Description

Please finish the assignment guided in the pdf. Database is in the excel.

You work for a popular pizzeria in suburban Rochester that has recently consideredproviding a guarantee on delivery times (e.g. Guaranteed delivery within 50 minutes, oryour pizza is free!). However, you are quite concerned about just how many pizzas youwill be giving away for free under such a policy. You shift manager claims that deliverytimes are uniformly distributed between 30 minutes and an hour, but you are not sosure about this. Luckily, you have been recording the actual delivery times for the pastseveral years and have assembled a dataset with 1400 observed actual delivery times(DeliveryTimes.xlsx).

a. Using the included dataset, compute the sample average, the sample standarddeviation and the sample variance of delivery time. You only need to reportthese three numbers here.b. Based on what you found in part a), are these findings consistent with deliverytimes being distributed uniformly between 30 and 60 minutes? Why or why not?Note: there is no need for a formal test here, just an informal discussion (forwhich the formulas for the mean and variance of a uniform distribution that youcan look up on Wikipedia will be useful).c. Suppose you assume instead that delivery times are normally distributed (ratherthan uniform) with the mean and standard deviation you found in part a). Usingthe estimates from part a), construct an interval into which you expect 95% ofdelivery times to fall. Repeat this exercise, but replace 95% with 80%. How dothese intervals compare with what you would have concluded had you justassumed that delivery times were distributed uniformly between 30 and 60minutes?d. Continuing to assume a normal distribution, what is the probability that a givenpizza is delivered in 45 minutes or less? How about 40 minutes or less? 50minutes or more? Compare these answers to what you would conclude underthe uniform assumption. e. If you were to implement a policy of only charging for pizzas that are delivered inunder 50 minutes, would it matter which distribution was the correct one? Whyor why not? (Note: you do not need to compute anything here, just answer thequestion from an intuitive standpoint).f. Again using the information from part a), construct a 95% confidence interval forthe population mean. How does this compare to the 95% interval youconstructed in part c (for the Normal case)? If it is different, what is the reasonfor this?g. Would the confidence interval you constructed in part f) change if you assumedthe population distribution was uniform instead of Normal? Why or why not?h. Using the information from part a), test the null hypothesis that the populationaverage delivery time is 50 minutes against the two-sided alternative hypothesisthat it is not 50 minutes at both the 1% and 5% levels. What do you conclude?

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