As long as your sample is large enough, you don't have to worry about using the sample standard deviation in place of the unknown population standard deviation in constructing a confidence interval because ________.
A) for low degrees of freedom, the t-distribution is similar to the standard normal distribution
B) for all degrees of freedom, the t-distribution is bell-shaped
C) for a large sample, the t-distribution is similar to the standard normal distribution
D) the sample standard deviation is an efficient estimator of the population standard deviation

Question

Quizplus · Accepted Answer

As per the Central Limit Theorem, for a large enough sample (usually considered when the sample size is greater than or equal to 30), the distribution of the sample means becomes approximately normal regardless of the shape of the population distribution. Therefore, when the sample size is large enough, the t-distribution is very similar to the standard normal distribution, and hence, we can use the sample standard deviation in place of the unknown population standard deviation while constructing the confidence interval.

As Long as Your Sample Is Large Enough, You Don't