A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality.A company that produces top-of-the-line batteries claims that its batteries are good, on average, for more than 65 months. A consumer protection agency tested 25 such batteries to check this claim. It found that the mean life of these 25 batteries is 63.4 months, and the standard deviation is 3 months. If we test the company’s claim at a 5% significance level, what is the p-value? Assume normality.0.00670.01350.99620.9933

Statistical hypothesis testing is an important method in inferential statistics. It is used to test the hypothesis about the population parameters. Statistical tests are used to calculate the test statistic and p-value. This test statistic and p-value will eventually be used to make decision on the rejection of null hypothesis.Let μ indicates the population average. Then the null and alternate hypotheses are given below. H0:μ=65H1:μ>65 It is given that x¯=63.4, s=3, n=25. Since the population standard deviation is unknown, t-statistic can be used. So the t statistic is calculated below. t=x¯-μsn=63.4-65325=-2.67 The test is right tailed, so for n-1=24 degrees of freedom, P(t>-2.67)=0.9933 is the p value. So option 4, 0.9933 is the correct answer.