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A boot has been designed which can be immersed for 12 hours without leaking. Five hundred pairs of the boots are tested and the time until first leakage is measured. The average time until first leakage for the sample is 12.25 hours with a standard deviation of 3.0 hours. Answer the following: 1) Find the p-value to test the claim that the average time until first leakage for the hunting boot is at least 12 hours.

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Answer:

0.0312

Step-by-step explanation:

Given :

Mean or average time, xbar = 12.25

Standard deviation, s = 3

Sample size, n = 500

The test statistic :

(x - xbar) ÷ (s/sqrt(n))

(12 - 12.25) ÷ 3/sqrt(500)

-0.25 ÷ 0.1341640

Test statistic = - 1.863

The Pvalue :

P(Z < - 1.863) = 1 - P(Z ≤ 1.863)

P(Z < - 1.863) = 0.0312

Hence, the Pvalue = 0.0312

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