Which of the following are the assumptions underlying the use of t-distribution?
(A) The variance of population is known.
(B) The samples are drawn from a normally distributed population.
(C) Sample standard deviation is an unbiased estimate of the population variance.
(D) It depends on a parameter known as degree of freedom.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (B) and (D) only
The t-distribution is used for small samples from a normal population when the population standard deviation is not known and has to be estimated from the sample.
Checking the statements
(A) The variance of population is known. — Incorrect. When the population variance is known, the normal (z) distribution is used. The t-distribution is needed precisely when it is unknown.
(B) The samples are drawn from a normally distributed population. — Correct. This is the basic assumption of the t-test.
(C) Sample standard deviation is an unbiased estimate of the population variance. — Incorrect. A standard deviation estimates a standard deviation, not a variance (the variance is its square), so the statement is not correct as worded.
(D) It depends on a parameter known as degree of freedom. — Correct. The shape of the t-distribution depends on its degrees of freedom, \(n - 1\) for a sample of size n.