Nutritional information provided by Kentucky Fried Chicken (KFC) claims that each small bag of potato wedges contains 4.8 ounces of food and 280 calories. A sample of ten orders from KFC restaurants in New York and New Jersey averaged 358 calories. Assume that the sample is approximately normally distributed. (a) If the sample deviation was s = 54 calories, is there sufficient evidence to indicate that the average number of calories in small bags of KFC potato wedges is greater than advertised? Clearly formulate the null and the alternative hypotheses, select an appropriate test and test at the 1% level of significance. (b) Compute the p-value of the test conducted in part (a). (c) Construct a 99% lower confidence interval for the true mean number of calories in small bags of KFC potato wedges. (d) On the basis of the interval computed in part (c), what would you conclude about the claim that the mean number of calories exceeds 280? How does your conclusion here compare with your conclusion in part (a) where you conducted a formal test of hypothesis?