From a recent production run of portable generators, you select a random sample

Question

From a recent production run of portable generators, you select a random sample of 10. You find that the average running time for the units in the sample is 24.4 hours, with a sample standard deviation of .6 hours. Use these sample results to test, at the 5% significance level, the null hypothesis that the average running time for the full population of generators is precisely 25 hours, no more and no less. Assume that the population of portable generators is normally distributed.

Please state the appropriate critical value that you would use to make the decision, state the test statistic that you calculate for this sample, and state whether or not you would reject the null hypothesis.

Explanation / Answer

hypothesis:

null: u = 25

alternate: u!=25

test static Z = 24.4 - 25/0.6/sqrt(10) = -3.16

critical values are -1.96 and 1.96

rejection region z < -1.96 and z > 1.96

hence reject null hypothesis

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