Is this true or false?
In an experiment involving matched pairs, a sample of 13 pairs of observations is collected. The degree of freedom for the t statistic is 11.
To determine whether the statement is true or false, we need to understand the concept of degrees of freedom in the context of a t-test for matched pairs.
In a matched pairs experiment, each observation in one group is paired with a corresponding observation in the other group. This allows for making a direct comparison between the two groups. The concept of degrees of freedom arises from the idea that the total number of observations in the sample is not entirely free to vary due to the pairing.
In this case, you are given that the sample consists of 13 pairs of observations. Since each pair has one observation in each group, the total number of observations in the sample is twice the number of pairs, which is 2 * 13 = 26.
The degrees of freedom for a t-test for matched pairs can be calculated as (N - 1), where N is the number of pairs. In this case, the degrees of freedom would be (13 - 1) = 12, not 11 as stated in the question.
Therefore, the statement is FALSE. The degree of freedom for the t statistic in this experiment is 12, not 11.