If the tabulated value of one sample t-test is given as: \( t_{16}(0.05)=2.12 \), then which of the following statements is/are correct ?
(A) Degrees of freedom are 16.
(B) Degrees of freedom are 17.
(C) The level of significance is 95%.
(D) The level of significance is 5%.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A) and (D) only
In the notation \( t_{\nu}(\alpha) \), the subscript ν is the number of degrees of freedom and α is the level of significance.
So \( t_{16}(0.05) \) means 16 degrees of freedom at the level of significance 0.05 = 5%.
Checking the statements
(A) Degrees of freedom are 16. — Correct. The subscript is 16.
(B) Degrees of freedom are 17. — Incorrect. 17 would be the sample size n; the degrees of freedom are n − 1 = 16.
(C) The level of significance is 95%. — Incorrect. 95% is the confidence level, 1 − 0.05.
(D) The level of significance is 5%. — Correct. α = 0.05 = 5%.