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
(A) The variance of population is known
This condition corresponds to the normal (z) distribution. The t-distribution is used when population variance is unknown.
False
(B) The samples are drawn from a normally distributed population
This is a basic assumption for applying the t-distribution, especially for small sample sizes.
True
(C) Sample standard deviation is an unbiased estimate of the population variance
This is a statistical property but not an assumption required for the validity of the t-distribution.
False
(D) It depends on a parameter known as degree of freedom
The shape of the t-distribution changes with degrees of freedom, which depend on sample size.
True
The correct options are (B) and (D).