If the alternate hypothesis states that u (Mu) does not equal 4,000, what is the rejection region for the hypothesis test?
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A. B. C. D. E.Explanation
The alternate hypothesis says does not equal, which means it could be less or more than 4000. So we must consider both tails.
In hypothesis testing, the rejection region refers to the range of values that would lead to the rejection of the null hypothesis. The null hypothesis (H0) is the default assumption or the statement being tested, while the alternative hypothesis (Ha) is the statement we are trying to gather evidence for.
In this case, the null hypothesis is that the population mean (μ) is equal to 4,000, while the alternative hypothesis states that μ does not equal 4,000. The alternate hypothesis does not specify whether the population mean is greater or smaller than 4,000; it only states that it is not equal.
To determine the rejection region, we need to consider the alternative hypothesis and the associated significance level (α) of the test. The significance level represents the maximum probability of making a Type I error, which is rejecting the null hypothesis when it is actually true. Commonly used significance levels include 0.05 (5%) and 0.01 (1%).
Since the alternative hypothesis is two-tailed (not equal), we need to consider both tails of the distribution. The rejection region will be split between the lower or left tail and the upper or right tail, denoting extreme values in either direction.
Therefore, the correct answer is option E: Both tails.