A substance used in biological and medical research is shipped by airfreight to users in cartons of 1,000 ampules. The data in the Excel file Quiz3.xlsx (Tab Air), involving 10 shipments, were collected on the number of times the carton was transferred from one aircraft to another over the shipment route (x) and the number of ampules found to be broken upon arrival (y). Assume that the first-order regression model given below is appropriate: y = beta0 + beta1 x + e
y x
16 1
9 0
17 2
12 0
22 3
13 1
8 0
15 1
19 2
11 0
Conduct a t-test to decide whether or not there is a linear association between number of times a carton is transferred (x) and number of broken ampules (y). Use a level of significance of 0.05. Clearly write every step of the hypothesis testing procedure.
Estimate the mean breakage for 4 transfers by constructing a 99% confidence interval. Interpret the confidence interval. Round your answer to 2 decimal places.
The next shipment will entail two transfers. Obtain a 99% prediction interval for the number of broken ampules for this shipment. Interpret this confidence interval. Round your answer to 2 decimal places.