The manufacturer of a certain brand of auto batteries claims that the mean life

Question

The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.40 months. The lives of all such batteries have a normal distribution with the population standard deviation of 4.5 months.

Find the p-value for the test of hypothesis with the alternative hypothesis that the mean life of these batteries is less than 45 months.

Round your answer to four decimal places.

Will you reject the null hypothesis at = 0.025?

Explanation / Answer

Here,

H0: 45

H1: < 45

z = (43.40 - 45)/4.5/24

z = - 1.74

P (z < 1.74) = 0.0409

p > 0.025

Thus, null is not rejected

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