if two dependent samples of size 20 are used to test the difference between the means, the degrees of freedom for a t-statistic is 19, true or false
true
In order to determine if the statement is true or false, let's understand how to calculate the degrees of freedom for a t-statistic.
The degrees of freedom for a t-statistic depends on the sample sizes of the two samples being compared. When dealing with dependent (or paired) samples, the degrees of freedom are calculated using the formula:
df = n - 1,
where "n" represents the sample size.
In the given question, two dependent samples of size 20 are being used for testing the difference between the means. Since the formula for calculating degrees of freedom is df = n - 1, the degrees of freedom for a t-statistic would be:
df = 20 - 1 = 19.
Therefore, the statement is true. The degrees of freedom for a t-statistic in this case would be 19.