AP Statistics · Unit 3 · Collecting Data

FreshCart Grocers wants to compare two insulated packaging liners, Liner S (standard) and Liner N (new design), to see which one better limits the rise in temperature of refrigerated groceries between warehouse pickup and customer delivery. The company will run the study on a batch of 40 upcoming refrigerated orders. Delivery route length varies widely: some orders travel on short routes (transit time under 20 minutes), while others travel on long routes (transit time over 45 minutes). For each order, a probe item is packed with a small thermometer, and the response variable is the temperature rise, in °F, of that item from the time it leaves the warehouse to the time it is delivered.

(a) In an earlier completely randomized pilot trial, among the 20 orders that used Liner S, the temperature rise ranged from 2°F on short routes to 14°F on long routes. Based on this result, explain why a randomized block design, with blocks based on route length, would be better than a completely randomized design for the full study.
(b) Of the 40 orders in the full study, 20 will travel on short routes and 20 on long routes. Describe how FreshCart could randomly assign the two liners to the 40 orders in a randomized block design with blocks based on route length, so that 10 orders in each block receive each liner.
(c) Suppose that, instead of randomly assigning liners within each route-length block, a warehouse manager assigns Liner S to every order packed by the morning shift and Liner N to every order packed by the afternoon shift. Explain why this method of assignment would prevent FreshCart from concluding that any observed difference in temperature rise was caused by the liner type rather than by some other factor.