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# Making conclusions in a t test for a mean

AP.STATS: DAT‑3 (EU), DAT‑3.F (LO), DAT‑3.F.1 (EK), DAT‑3.F.2 (EK)

## Problem

A local pizza store knows the mean amount of time it takes them to deliver an order is 45 minutes after the order is placed. The manager came up with a new system for processing delivery orders, and they were curious if it changed the mean delivery time. They took a sample of 40 delivery orders to test H, start subscript, 0, end subscript, colon, mu, equals, 45 minutes versus H, start subscript, start text, a, end text, end subscript, colon, mu, does not equal, 45 minutes, where mu is the mean delivery time under the new system.
The delivery times in the sample had a mean of 48 minutes and a standard deviation of 8 minutes. These results produced a test statistic of t, approximately equals, 2, point, 37 and a P-value of approximately 0, point, 023. Assume that the conditions for inference were met.
Is there sufficient evidence at the alpha, equals, 0, point, 05 level to conclude that the mean delivery time has changed from 45 minutes?