# Independent samples t-test for difference in means

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The makers of Bounce Back glass backboards for basketball gymnasiums have claimed that their board is at least as durable, on the average, as the leading backboard made by Swoosh Company. Products Testing Services of Des Moines, Iowa, was hired to verify this claim. It selected a random sample of 50 backboards of each type and subjected the boards to a pressure test to determine how much weight hung from a basketball rim it would take to break the fiberglass backboard. The following results were determined from the testing process.

SWOOSH BOUNCEBACK

m= 691 lb m = 653 lb

s = 112 lb s = 105 lb

In your groups, complete the following tasks.

a. Assuming that the more pounds needed to break the backboard, the better it is, state the appropriate null and alternative hypotheses.

b. At a significance level of 0.01, what conclusion should be reached with respect to the claim made by the Bounce Back Company? Discuss.

c. Suppose the hypothesis test was conducted at a significance level of 0.10 instead of 0.01. Would this change the conclusion reached based on the sample data? If so, discuss why; if not, discuss why not.

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This is a large sample, independent samples, hypothesis test (t-test) for the difference between two population means. The explanation shows how the significance level (alpha) affects the decision we make when we test hypotheses.

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