For a one-sample t-test with sample size n, the degrees of freedom are:

For a one-sample t-test with sample size n, the degrees of freedom are:

• A. n minus 1
• B. n
• C. n minus 2
• D. 2

Answer: (A)

Degrees of freedom in a one-sample t-test reflect how many values can vary once the sample mean is fixed. Because you use the data to estimate the mean, one degree of freedom is consumed, leaving n−1 independent pieces of information to estimate the variability and form the t statistic. The test statistic is t = (X̄ − μ0) / (s/√n), and the standard deviation s is computed from the sample with denominator n−1, which ties directly to having n−1 degrees of freedom. If you used n, it would ignore the loss of freedom from estimating the mean; n−2 would apply in scenarios where two parameters are estimated, which isn’t the case here.

Degrees of freedom in a one-sample t-test reflect how many values can vary once the sample mean is fixed. Because you use the data to estimate the mean, one degree of freedom is consumed, leaving n−1 independent pieces of information to estimate the variability and form the t statistic. The test statistic is t = (X̄ − μ0) / (s/√n), and the standard deviation s is computed from the sample with denominator n−1, which ties directly to having n−1 degrees of freedom. If you used n, it would ignore the loss of freedom from estimating the mean; n−2 would apply in scenarios where two parameters are estimated, which isn’t the case here.