Question 5: (15 points) A company claims the average content of containers of a

particular lubricant is 10 liters. The contents (unit: liter) of a random sample of 10

containers are the following: 10.3, 9.8.,10.2,9.7,10.3,10.1,9.8,9.9,10.4,10.1, Assume

that the distribution of contents is normal. Is the claim by the company correct?

That is, is there evidence that the average content of the containers of a particular

lubricant is 10 liters? (a) Conduct a hypothesis test at a level of a = 0.1, making

sure to state your conclusion in the context of the problem. (Hints: use t model

and consider a 2-sided alternative hypothesis) (b) Construct and interpret a 90%

confidence interval for the average content of containers and see whether it confirms

the conclusion of hypothesis test.