A student wants to know why we use a tdistribution instead o

A student wants to know why we use a t-distribution instead of a normal distribution to construct a confidence interval? Which statements below are correct?

(A) For large sample sizes (say over 100), it does not make much difference whether we construct the confidence interval using the normal or the t-distribution, they will both be very similar.

(B) We use a t-distribution instead of a normal distribution when we estimate the standard deviation from the data. It is used to correct for the underestimation of the true population standard deviation.

(C) We use a t-distribution instead of a normal distribution when the sample size is small and we do not know whether the central limit theorem holds.

(D) A and B

(E) A and C

Solution

It is OPTION D: A and B.

[Option C is false because we always know that the central limit theorem always holds, it\'s just that for small sample size, the approximation of a normal distirbution may not be that good yet.]