Question

If the alternative hypothesis includes the symbol <, the rejection region is in the upper tail. Group of answer choices True False

Answer 1

The statement is False because if the alternative hypothesis includes the symbol <, the rejection region is in the lower tail.

Step-by-step explanation:

If the alternative hypothesis includes the symbol <, the rejection region is actually in the lower tail, not the upper tail. This is because the alternative hypothesis indicates the direction in which we suspect the true parameter lies if it is not equal to the value stated in the null hypothesis. For example, if the null hypothesis is H_o: μ ≤ 15 and the alternative hypothesis is Ha: μ > 15, we are looking for evidence that μ is greater than 15, meaning the rejection region would be in the upper tail of the distribution. However, if the alternative hypothesis were Ha: μ < 15, we would look for evidence that μ is less than 15, so the rejection region would be in the lower tail. Therefore, the correct answer to the question is False.

Answer 2

If the alternative hypothesis includes the symbol <, the rejection region is in the upper tail is True.

Step-by-step explanation:

The statement is true. The placement of the rejection region in hypothesis testing depends on the direction of the alternative hypothesis. If the alternative hypothesis includes the symbol < (less than), it implies that we are interested in detecting a decrease or reduction in a parameter. In this case, the rejection region is in the upper tail of the distribution.

When testing a hypothesis, we set up a null hypothesis
`(\(H_0\))` and an alternative hypothesis
`(\(H_1\))`. The null hypothesis typically includes a statement of no effect or no difference, while the alternative hypothesis indicates the direction and nature of the effect we are trying to detect. If the alternative hypothesis suggests a less-than relationship, the rejection region is in the upper tail because we are looking for evidence of a decrease or reduction.

For example, in a one-tailed test where the alternative hypothesis is
`(H_1: \mu < \mu_0\)`(indicating a decrease in the population mean), the rejection region will be in the upper tail of the distribution. This region is chosen based on the chosen level of significance
`(\(\alpha\))` and critical values. The rejection region in the upper tail signifies the extreme values of the test statistic that would lead to rejecting the null hypothesis in favor of the alternative hypothesis.