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.
DF = n - 1
...where n is the number of paired observations.
To determine if this statement is true or false, we need to understand the concept of degrees of freedom and how they are applied in the context of the t statistic for matched pairs experiments.
In a matched pairs experiment, two sets of observations are collected, with each pair consisting of two related measurements, such as before and after measurements on the same subjects. The purpose of the experiment is to compare the means of the two sets of measurements.
The t statistic for matched pairs is calculated using the formula:
t = (mean difference)/ (standard deviation of the differences divided by the square root of the sample size)
The degrees of freedom (df) for the t statistic in a matched pairs experiment is given by the formula:
df = n - 1
where n is the number of pairs of observations.
In this case, the statement mentions that a sample of 13 pairs of observations is collected, so n = 13. Therefore, the degrees of freedom for the t statistic in this scenario would be:
df = 13 - 1 = 12
Since the given statement incorrectly states that the degrees of freedom for the t statistic is 11, the statement is false. The correct answer is false.