When would you use a t-distribution?

When would you use a t-distribution?

• A. With a small sample
• B. With a large sample
• C. Only when the population standard deviation is known
• D. Only for binomial data

Answer: (A)

When estimating a population mean from a sample with an unknown population standard deviation, you use the t distribution. This situation is most common with a small sample, because you’re replacing the true sigma with the sample standard deviation, which adds extra uncertainty. The t distribution accounts for that by having heavier tails, making confidence intervals wider and using larger critical values when n is small. As the sample size grows, the estimate of sigma becomes more reliable, and the t distribution looks more like the normal distribution. If sigma were known, you’d use the normal distribution instead. It isn’t used for binomial data, where a binomial model or a normal approximation would be more appropriate.

When estimating a population mean from a sample with an unknown population standard deviation, you use the t distribution. This situation is most common with a small sample, because you’re replacing the true sigma with the sample standard deviation, which adds extra uncertainty. The t distribution accounts for that by having heavier tails, making confidence intervals wider and using larger critical values when n is small. As the sample size grows, the estimate of sigma becomes more reliable, and the t distribution looks more like the normal distribution. If sigma were known, you’d use the normal distribution instead. It isn’t used for binomial data, where a binomial model or a normal approximation would be more appropriate.