Question

A battery company claims that its batteries last an average of 100 hours under normal use. After several complaints that the batteries do not last this long, an independent testing laboratory decided to test the company’s claim with a random sample of 42 batteries. The data from the 42 batteries appeared to be unimodal and symmetric with a mean 97 hours and a standard deviation of 12 hours. Is this evidence that the company’s claim is false and these batteries actually last less than 100 hours? What would be a Type I Error in the context of this problem?

Answer 1

Below are the null and alternative Hypothesis,
Null Hypothesis, H0: μ = 100
Alternative Hypothesis, Ha: μ < 100

Test statistic,
t = (xbar - mu)/(s/sqrt(n))
t = (97 - 100)/(12/sqrt(42))
t = -1.62

P-value Approach
P-value = 0.0564

As P-value >= 0.05, fail to reject null hypothesis.

There is not sufficient evidence to conclude that the mean life of battery is not less than 100 hours.

Type I error occurs if the conclusion made is that the life of battery is less than 100 hours however in actual it is equal to 100 hours.