Peter's cat, Piper, is a finicky eater. Peter is trying to determine which of two brands of canned cat food Piper prefers, Pick-a-Pair or Pickled Peppers. For two months, he flips a coin each day to decide which of the two foods to feed Piper, and weighs how much Piper eats (in grams). Here are the data:

n x s

Pick-a-Pair 31 85.2 3.45

Pickled Pappers 30 82.1 4.62

(a) Construct and interpret a 99% confidence interval for the difference in mean amount of food Piper eats when she is offered Pick-a-Pair and when is offered Pickled Peppers.

(b) Suppose we want to test the hypothesis that the mean amount of Pick-a-Pair that Pickles eats is higher than the mean amount of Pickled Peppers she eats. State the null and alternative hypotheses for this test.

(c) The standardized test statistic is t=2.96 and the P-value is 0.002. Draw an appropriate conclusion using = 0.01.