Textbook Question
In Exercises 3–8, find the critical value(s) and rejection region(s) for the type of t-test with level of significance alpha and sample size n.
Left-tailed test, α=0.10, n=38
50
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9. Hypothesis Testing for One Sample
Critical Values and Rejection Regions
Multiple Choice
Mark ‘TRUE’ or ‘FALSE’ for each of the following.
The critical value is the boundary of the rejection region.
A
TRUE
B
FALSE
C
Cannot be determined
Verified step by step guidance1
Understand the concept of a critical value in hypothesis testing: it is the value that separates the rejection region from the non-rejection region on the sampling distribution.
Recall that the rejection region is the set of all values of the test statistic that would lead us to reject the null hypothesis.
Recognize that the critical value acts as the boundary point between the rejection region and the acceptance region.
Therefore, the critical value marks the exact cutoff point where the decision changes from not rejecting to rejecting the null hypothesis.
Conclude that since the critical value defines the boundary of the rejection region, the statement 'The critical value is the boundary of the rejection region' is TRUE.
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