Which of the following is true of the t-distribution?
A) It has narrower confidence intervals than the standard normal distribution.
B) It is only used to calculate confidence intervals where there is no known population standard deviation.
C) It converges to the standard normal distribution as degrees of freedom increase.
D) It does not require parameters such as degrees of freedom.

Question

Quizplus · Accepted Answer

The t-distribution approaches the standard normal distribution as degrees of freedom increase. This means that as sample size increases, the t-distribution becomes closer to the standard normal distribution. Option A is incorrect because the t-distribution has wider confidence intervals than the standard normal distribution due to greater uncertainty when estimating the population standard deviation from the sample standard deviation. Option B is incorrect because the t-distribution is used specifically for calculating confidence intervals when the population standard deviation is unknown. Option D is incorrect because the t-distribution is a parameterized distribution that requires degrees of freedom as a parameter.

Which of the Following Is True of the T-Distribution