HELP PO!
If the computed z-value is -1.290 and the critical value is -2.571, which of the following statements could be true?
A. It lies in the rejection region, H must be rejected.
B. It lies in the rejection region, we failed to reject H.
C. It lies in the non-rejection region, H must be rejected.
D. It lies in the non-rejection region, we failed to reject H.
Answers
Answer:
D. It lies in the non-rejection region, we failed to reject H. It is the correct option.
Assume that this is the usual normal distribution. We know our test statistic follows the standard normal because it is a computed Z value. We also know the critical value is minus 2.571, therefore it's somewhere around here. As a result, if our test statistic was anyplace to the left or more extreme than the critical number, we would reject the null hypothesis. Our test statistic, however, is -1.29, which is not as extreme as the threshold figure. As a result, the null hypothesis is not rejected. In other words, it is in the non-rejection area, and the null hypothesis was not rejected. So D is the proper answer.
Answer:
Option (D) It lies in the non-rejection region, we failed to reject H.
Step-by-step explanation:
Suppose that this is a normal distribution.
- Now, since it is a computed Z value, we know the test statistic follows the standard normal.
- The critical value is equal to .
- As a corollary of this, the test statistic would be anywhere to the left, we would reject the null hypothesis.
- However, our test statistic value is . Clearly, this value is less extreme than the threshold value. This is the reason why the null hypothesis will not be rejected.
Hence, it lies in the non-rejection region, and we fail to reject H.
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