Suppose you work at the legal department of a firm that makes packets of sugar. To avoid any lawsuits, the legal department wants to ensure that the mean weight of sugar packets is greater than 10 grams. Your goal is to formulate and perform an hypothesis test that will help strongly support this conclusion. (a) (5 points) Formulate an appropriate hypothesis test by stating clearly your choice of the null hypothesis and the alternative hypothesis. Explain the reason behind your choice. (b) (5 points) You weigh 25 such sugar packets, and obtain the sample mean x = 10.93grams and the sample standard deviation s = 2.52 grams. Using the significance level of a = 0.05, perform the hypothesis test and state your conclusions. Provide clear justification for how you reached your conclusion.