Construct a 95% confidence interval for . Make sure to show your work. Also, interpret your confidence interval in context.
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. Construct a 95% confidence interval for . Make sure to show your work. Also, interpret your confidence interval in context.
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