Jordan's cat "Fern" is a finicky eater. Jordan is trying to determine which of two brands of canned cat food Fern prefers, Tab-a-Cat or Chow Lion. For two months, she flips a coin each day to decide which of the two foods to feed Fern, and weighs how much Fern eats in grams. Here is the data: XS 85.2 3.45 n Tab-a-Cat 31 Chow Lion 30 82.1 4.62 (a) Find the standard error for the difference in the mean amount of Tab-a-Cat that Fern eats and the mean amount of Chow Lion she eats. (b) Construct and interpret a 99% confidence interval for the difference in mean amount of food Fern eats when she is offered Tab-a-Cat and when she is offered Chow Lion. c) Suppose we want to test the hypothesis that the mean amount of Tab-a-Cat Fern eats is higher than the mean amount of Chow Lion she eats. State the null and alternative hypotheses for this test. d) The test statistic is t = 2.962. Determine the P-value and draw an appropriate conclusion using =0.01.