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: 10.2,9.7,10.1,10.3,10.1,9.8,9.9,10.4,10.3,9.8. 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 α=0.05, making sure to state your conclusion in the context of the problem. (Hints: use t model and consider a two-sided alternative hypothesis) Step 1: State null and alternative hypothesis. Step 2: Assumptions and conditions check, and decide to conduct a one-sample t-test. Step 3: Compute the sample statistics and find p-value. Step 4: Interpret you p-value, compare it with α=0.05 and make your decision. (b) Construct and interpret a 95\% confidence interval for the average content of containers. Does this confidence interval support your result in (a)? (Hints: construct a one-sample t-interval and be sure the appropriate assumptions and conditions are satisfied before you proceed. )