Question 1 A researcher wants to study the fat contents in Burgers from two restaurants: Joe's and Frank's. He randomly buy 15 burgers from each of these two restaurants and measure the fat contents in each burger. The collected data is in the file FatContent.txt. Assuming both population distributions are normal with the same variance. a) The researcher wants to know if the mean fat contents are the same for those two restaurants. State the null and alternative hypotheses. Calculate the test statistic and give the p-value of the test. State the conclusion of the hypothesis test at a = 0.05 significance level. b) Calculate a 99% confidence interval for the difference between the true mean fat con- tents of Joe's and Frank's restaurants. Based on the results in part (b), do we reject the null hypothesis that the difference between the true mean fat contents of Joe's and Frank's restaurants is -3 at a = 0.01? Justify your answer.