Two adhesives for pasting plywood boards are to be compared. 10 tubes are prepared using Adhesive I and 8 tubes are prepared using Adhesive II. Then 18 different pairs of plywood boards are pasted together, one tube per pair of boards.

(a) The response is the time in minutes for the boards to stick together, and the summary statistics are

Should you or should you not pool the estimates of variance in order to conduct a test of hypotheses that is intended to show that there is a difference in means? Explain how you would proceed.

(b) Conduct the test for part (a) using \(\alpha=0.01\).

(c) Describe how you would randomize the assignment of adhesives when conducting this experiment.

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Sample Standard size Mean deviation Adhesive I Adhesive II 10 8.5 8 9.25 0.9 2.6