NO.PZ2023061301000009
问题如下：
Which of the following statements regarding a one-tailed hypothesis test is
correct?
选项：
A.The rejection region increases in size as the level of significance becomes
smaller.
B.A one-tailed test more strongly reflects the beliefs of the researcher than a
two-tailed test.
C.The absolute value of the critical value is larger than that for a two-tailed
test at the same level of significance.
解释：
B is correct. One-tailed tests in which the alternative is “greater than” or “less
than” represent the beliefs of the researcher more firmly than a “not equal to”
alternative hypothesis.
A is incorrect because a smaller significance level implies a smaller rejection
region. C is incorrect because the absolute value of the critical value for a
one-tailed hypothesis test is smaller than that of a two-tailed test.
For example, for a two-tailed t-test with 30 degrees of freedom at the 5% significance
level, the corresponding critical value is ±2.042 (2.5% in each tail) whereas
the corresponding critical value for a one-tailed t-test is +1.697 or –1.697 (5%
in the left or right tail). Thus, the absolute value of the critical value is smaller
for the one-tailed test than it is for the two-tailed test for the same level of
significance.
同样的置信区间，单尾的critical value要小于双尾么
