Which of the following statements is most nearly correct,other things being equal?
A) Using Student's t instead of z makes a confidence interval narrower.
B) The table values of z and t are about the same when the mean is large.
C) For a given confidence level,the z value is always smaller then the t value.
D) Student's t is rarely used because it is more conservative to use z.

Question

Quizplus · Accepted Answer

For a given confidence level, the t value is always larger than the z value because the t distribution has heavier tails than the z distribution. This means that there is more variability in the t distribution, which requires larger critical values for a given level of confidence. Therefore, statement C is the most nearly correct. Statements A, B, and D are incorrect because using Student's t instead of z makes a confidence interval wider (not narrower), the table values of z and t differ in magnitude regardless of the mean, and Student's t is used when the population standard deviation is unknown or the sample size is small (not because it is more conservative to use z).

Which of the Following Statements Is Most Nearly Correct,other Things