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)?
Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...
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