Question

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.​​

Answer 1

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 2

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 $-2.571$.
• 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 $-1.290$. 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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