Which of the following statements are true?
A) Knowledge of the test statistic's distribution when the null hypothesis is true allows us to construct a rejection region for which the type I error probability is controlled at the desired level.
B) The rejection region for the t test differs from that for the z test only in that a t critical value replaces the z critical value.
C) If $X _ { 1 } , X _ { 2 } , \ldots \ldots , X _ { n }$
(n is small) is a random sample from a normal distribution, the standardized variable $T = ( \bar { X } - \mu ) / ( S / \sqrt { n } )$
Has a t distribution with n-1 degrees of freedom.
D) All of the above statements are true.
E) None of the above statements are true.

Question

Quizplus · Accepted Answer

A) This is a fundamental concept in hypothesis testing, where the distribution of the test statistic under the null hypothesis is used to determine the critical values or rejection region that controls the Type I error rate. B) The main difference between the t test and the z test is indeed the use of the t distribution instead of the normal distribution, which accounts for the increased variability (and thus uncertainty) when estimating the standard deviation from a small sample. C) This statement accurately describes the calculation and distribution of the t statistic when the sample size is small and the population is normally distributed.

Which of the Following Statements Are True? A) Knowledge of the Test

Which of the Following Statements Are True?
A) Knowledge of the Test