The glycemic index (GI) is a rating system for foods containing carbohydrates. It shows how quickly each food affects your blood sugar (glucose) level when that food is eaten on its own.

A random sample of 33 children were provided with a breakfast of low GI foods on one day and high GI foods on another. The two breakfasts contained the same quantities of carbohydrate, fat and protein. On each day a buffet lunch was provided, and the number of calories eaten at lunchtime were recorded. On the first day the children ate a low GI breakfast and on the second day a high GI breakfast.

Let be the true mean of the differences in calorie intake for a high GI and a low GI breakfast, respectively. The researcher wants to conduct inference on ​ to determine whether the kind of breakfast eaten has an effect on mean calorie intake. The differences are calculated as calorie intake after high-GI breakfast minus calorie intake after low-GI breakfast. The sample mean of the differences of 63.543 calories, and the sample standard deviation of the differences was 153.523 calories.


A. Briefly (in 1-2 sentences) explain why we must use inference procedures for paired data instead of inference procedures for independent random samples. (Note: We will read only the first up to 2 sentences of your answer, so it will not help you to write more than 2 sentences.)

B. What are the symbol for and the value of the point estimate for the true mean of the differences in calorie intake for the children (high GI – low GI)?