Larger Z-Statistic Critical Value

Larger Z-Statistic Critical Value

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Question

The larger the critical value on the z-statistic,

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A. B. C. D. E.

B

To reject a null hypothesis, the z-statistic must be larger in magnitude than the critical value for a given level of significance.

The correct answer is D. the easier it is to reject the null hypothesis.

In hypothesis testing, the null hypothesis represents the default assumption or the claim that there is no significant difference or relationship between variables. The alternative hypothesis, on the other hand, is the claim that contradicts the null hypothesis and suggests the presence of a significant difference or relationship.

When conducting hypothesis testing using the z-statistic, the critical value is a threshold that determines the level of significance at which we can reject the null hypothesis. The critical value is based on the desired level of significance (often denoted as α) and the degrees of freedom associated with the test.

If the calculated z-statistic falls beyond the critical value, it means that the test statistic is extreme enough that the probability of obtaining such a result by chance (assuming the null hypothesis is true) is very low. In this case, we reject the null hypothesis in favor of the alternative hypothesis.

Now, when the critical value on the z-statistic is larger, it means that the threshold for rejecting the null hypothesis is higher. In other words, the larger the critical value, the more extreme the test statistic needs to be in order to reject the null hypothesis. This implies that it becomes easier to reject the null hypothesis because the criteria for rejecting it become less stringent.

Therefore, option D is the correct answer: the larger the critical value on the z-statistic, the easier it is to reject the null hypothesis.