In order to test the following hypotheses at an α level of significance H0: μ ≤ 800
Ha: μ > 800
The null hypothesis will be rejected if the test statistic Z is

Question

In order to test the following hypotheses at an α level of significance H0: μ ≤ 800
Ha: μ > 800
The null hypothesis will be rejected if the test statistic Z is
A) ≥ Zα
B) < Zα
C) < -Zα
D) = α

Quizplus · Accepted Answer

The alternative hypothesis, Ha, is a one-tailed hypothesis with the symbol ">" which means we are testing if the population mean is "greater than" 800. In order for us to reject the null hypothesis, H0, we need to have strong evidence that supports Ha. This means we need to find a test statistic, Z, that is large enough to fall in the rejection region (i.e. the tail of the distribution) of the standard normal distribution.

At an α level of significance, the critical value (or cutoff value) for the right tail of the standard normal distribution is Zα. Since we are testing Ha and we want to reject H0 when μ > 800, the rejection region is in the right tail of the distribution, which means the test statistic Z needs to be larger than Zα in order for us to reject H0.

Therefore, the correct choice is A which says that the null hypothesis will be rejected if the test statistic Z is greater than or equal to Zα.

In Order to Test the Following Hypotheses at an α