Consider the following hypothesis test:
\( \mathrm{H_0}:\mu\le 12 \)
\( \mathrm{H_a}:\mu\gt 12 \)
A sample of 25 provided a sample mean \( \overline{x}=14 \) and a sample standard deviation \( s=4.32 \). The degree of freedom is
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 24
The test concerns one population mean with the standard deviation estimated from the sample, so it is a one-sample t-test. Its degrees of freedom are
\( \displaystyle \nu=n-1=25-1=24 \)
The degrees of freedom depend only on the sample size; the values of \( \overline{x} \), s and the hypotheses do not affect them.
CBSE Applied Mathematics (Class XII):
Degrees of Freedom
