true or false if there were 15 difference scores in a matched pairs design then there were 28 participants in the study

15 * 2 = 30

A nurse at a local hospital is interested in estimating the birth weight of infants. How large a sample must she select if she desires to be 99% confident that the true mean is within 2 ounces of the sample mean? The standard deviation of the birth weights is known to be 7 ounces.

To determine whether the statement is true or false, we need to understand the concept of a matched pairs design and the relationship between difference scores and participants.

In a matched pairs design, each participant is measured twice under different conditions. The primary objective is to compare the scores of the same participant under these two different conditions. The difference between the scores of each participant is referred to as a "difference score." These difference scores represent the change in scores or performance between the two conditions.

To find out the number of participants, we can divide the total number of difference scores by 2 because each participant contributes one difference score. So, if there were 15 difference scores, we can conclude that there were 15/2 = 7.5 participants in the study.

Since the concept of half a participant is not possible, it can be concluded that the statement "if there were 15 difference scores in a matched pairs design, then there were 28 participants in the study" is false.