Delphi Pizza

Delphi Pizza is a family owned pizza restaurant, established and operated by Eliza C. and it serves a cluster of villages in the Laurentians. Delphi Pizza has been in operation for 15 years and was the first pizza restaurant in the area to offer delivery as well as dine-in pizza. Recently one of the national chains of fast-food pizza found its way to a nearby town. In order to attract business the new competitor guarantees delivery of its pizzas within 30 minutes after an order is placed. If the delivery is not made within 30 minutes, the customer receives the order without charge. Before long, there were signs that this new pizza restaurant was taking business away from Delphi Pizza. Eliza realized that Delphi would have to offer a similar guarantee to remain competitive. In order to formulate this offer Eliza knew she needed to collect data on Delphi Pizza deliveries. Over the course of a month Eliza collected data on 240 deliveries. The data is contained in the file Pizza.xlsx. The variables in the file are defined as follows:

DAY: Day of the week (1=Monday, 7=Sunday)

HOUR: Hour of the day (4-11pm, the hours when Delphi Pizza is open)

PREP_TIME: Time required (in minutes) to prepare the order

WAIT_TIME: Time (in minutes) from completing preparation of the order until a delivery person was available to deliver the order

TRAVEL_TIME: Time (in minutes) it took the car to reach the delivery location

DISTANCE: Distance (in kilometers) from Delphi Pizza to the delivery location

Eliza has asked you for some assistance interpreting the data. You will first have to help her by creating a new variable called TOTAL_TIME, which is the sum of PREP_TIME, WAIT_TIME and TRAVEL_TIME and which represents the time from the call being received to the delivery being made. This is the time to which the guarantee will be applied.

  1. Is there sufficient evidence to conclude that the average time to deliver a pizza, from the time of the phone call to the time of delivery, is greater than 25 minutes? Use a level significance of your choice, perform an appropriate statistical analysis.
  2. Estimate the percentage of deliveries which take more than 29 minutes with a 98% confidence interval. If a guarantee of delivery in less than 29 minutes or free pizza is made, what does this confidence interval imply for the percentage of customers who would get free pizza?
  3. Compute 98% confidence intervals for the average delivery times for the different days of the week. Would you make a recommendation for hiring more people on certain days?
  4. Write a report based on your findings.