i. The test statistic t has n-1 degrees of freedom. ii. All t distributions have the same mean of zero and a standard deviation of 1.
iii. The t distribution is more spread out and flatter at the center than is the standard normal distribution. However, as the sample size increases, the t distribution curve approaches the standard normal distribution.
A) (i), (ii), and (iii) are all correct statements.
B) (iii) is a correct statement but not (i) or (ii).
C) (i) and (iii) are correct statements but not (ii).
D) (ii) and (iii) are correct statements but not (i).
E) (i), (ii), and (iii) are all false statements.

Question

Quizplus · Accepted Answer

- Statement (i) is correct because the degrees of freedom for a t-test are indeed n-1, where n is the sample size.- Statement (ii) is incorrect because while all t distributions have a mean of zero, they do not all have a standard deviation of 1. The standard deviation of a t distribution varies depending on the degrees of freedom and is greater than 1.- Statement (iii) is correct as it accurately describes the shape of the t distribution compared to the standard normal distribution and its convergence to the normal distribution as sample size increases.

I the Test Statistic T Has N-1 Degrees of Freedom