Suppose that a researcher is studying a food delivery app. They claim that the app’s actual delivery time is 5 minutes longer than the estimated delivery time on average. To study this the researcher randomly selects 11 deliveries and records their estimated delivery time and their actual delivery time. They get the

A First Course in Probability (10th Edition)
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Chapter1: Combinatorial Analysis
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Suppose that a researcher is studying a food delivery app. They claim that the app’s actual delivery time is 5 minutes longer than the estimated delivery time on average. To study this the researcher randomly selects 11 deliveries and records their estimated delivery time and their actual delivery time. They get the following data. (Note: You may assume there were many deliveries to choose from.)

Estimated Delivery Time 25
35
15
30
25
30
15
50
10
40
30

Actual Delivery Time 43
35
25
44
36
50
18
60
16
51
38

(a) Carry out a hypothesis test at α = .05 to test the claim that the difference in actual and estimated delivery time is more than 5 minutes on average.

(b) Build a 95% confidence interval for the average difference between estimated delivery and actual delivery time.

(c) Would deciding that the average difference in actual and estimated delivery time is greater than 5 minutes on average when in reality it is not be a Type 1 Error or a Type 2 Error?

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