i. The test statistic for a problem involving an unknown population standard deviation is the Student's t distribution. ii. The t distribution approaches the Z distribution as the sample size increases.
iii. As the sample size increases, the computed value of t decreases.
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

(i) When the population standard deviation is unknown, the Student's t distribution is used as the test statistic. (ii) The t distribution does indeed approach the Z distribution as the sample size increases, becoming practically the same at large sample sizes. (iii) The statement about the computed value of t decreasing as the sample size increases is a misunderstanding; the value of t depends on the sample data and the hypothesis being tested, not directly on the sample size. However, the critical values of t (for a given significance level) approach those of the Z distribution as sample size increases, which might be the source of confusion.

I the Test Statistic for a Problem Involving an Unknown