A consumer testing organization wants to know whether two brands of work shoes have equally long-lasting heels. Tests show that 50 randomly selected workers wore out the heels of Brand X shoes, on average, in 96 days with a standard deviation of 6.4 days, while 50 randomly selected workers wore out the heels of Brand Y shoes, on average, in 99 days with a standard deviation of 6.1 days. (a) Test at the level of significance a = 0.05 whether the difference between the two average wearing lives is significant. (b) Compute the p-value and use it to decide whether the difference between the sample means is significant at the 0.05 level of significance.

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