The fill volume of a particular lubricant is normally distri

The fill volume of a particular lubricant is normally distributed with a mean of 10 liters. Suppose we randomly select 10 containers and we find that the sample mean is 10.06 liters and the sample standard deviation is 0.25 liters. You are asked to conduct a hypothesis test at the alpha = 0.05 level of significance to determine if the mean fill volume of the lubricant is greater than 10 liters. What null and alternative hypotheses would you use to conduct this test? What type of test statistic would you use to conduct this test? If you were to use a confidence interval rather than a hypothesis test to determine if the mean fill volume of the lubricant is greater than 10 liters, what would be your best choice for a confidence interval so that it directly corresponds to the hypothesis test? If your confidence interval covers 10, your decision and conclusion would be which of the following.

Solution

Given µ = 10n=10x = 10.06s = 0.25

The null hypothesis test at = 0.05 level of significance is

Against the alternative hypothesis

The test statistic t is given by

t = (x- µ)/(s/n-1) t_(n-1)

t = (10.06- 10)/(0.25/10-1) t_(10-1)

t = (0.06)9/0.25 t₍₉₎

therefore t_tab at 9 degrees of freedom at = 0.05 level of significance is 1.833

therefore t_cal < t_tab we accepted the null hypothesis

we use 95% one sided lower bound

desion is do not reject null hypothesis

conlusion we have enough evidence at the = 0.05 level of significance to show that the mean volume is less than 10 l;iters