4. The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 month. A consumer protection agency that wants to check this claim took a random sample of 36 such batteries and found the mean life for this sample is 43.75 month with a standard deviation of 4 month. Using the 2.5% significance level, test the manufacturer claim against the alternative that the mean life of batteries is less than 45 month.

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