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 Gl foods on one day and high Gl 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 Gl breakfast and on the second day a high Gl breakfast. Let Hd be the true mean of the differences in calorie intake for a high Gl and a low GI breakfast, respectively. The researcher wants to conduct inference on Hd 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.
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.)
