Consumer Reports tested 14 brands of vanilla yoghourt and found the following numbers of calories per serving:160 200 220 230 120 180 140130 170 190 80 120 100 170

a. State all the necessary assumptions and report a 90% confidence interval for the mean calorie content of vanilla yogurt.

b. A diet guide claims that you will get an average of 120 calories from a serving of vanilla yogourt. Based on the given data, is there evidence that the mean calorie content is different from the claim of the diet guide?