Question

Which of the following statements is (are) true regarding 1-tailed and 2-tailed hypothesis tests? Check all that apply.

Note: Consider this carefully. There may be more than one correct answer and there is no partial credit for getting only one selection correct. Also note that, when considering a 1-tailed test, assume that we are excluding the possibility of getting a test statistic in the 'wrong' tail, i.e. the tail which does not contain the critical value.
Rejecting a 1 tailed test implies that you would fail to reject the corresponding 2 tailed test at the same α level
Rejecting a 1-tailed test implies that you would also reject the corresponding 2-tailed test at the same significance level
Failing to reject a 2-tailed test implies that you would also fail to reject the corresponding 1-tailed test at the same significance level
Rejecting a 2-tailed test implies that you would also reject the corresponding 1-tailed test at the same significance level
Failing to reject a 2-tailed test means that you will reject the corresponding single tailed test at the same α level
Failing to reject a 1-tailed test implies that you would fail to reject the corresponding 2-tailed test at the same alpha level

Answer 1

Rejecting a 1-tailed test implies rejection of a 2-tailed test at the same α level, failing to reject a 2-tailed implies failure to reject a 1-tailed, and the vice versa for both situations. Some statements are true, while others are false, regarding the implications of rejection or non-rejection between 1-tailed and 2-tailed tests.

Step-by-step explanation:

When discussing 1-tailed and 2-tailed hypothesis tests, it is important to understand the relationship between the rejection of the null hypothesis and the significance level (α) chosen. For 1-tailed tests, rejecting the null implies we have statistical evidence in one specified direction. For 2-tailed tests, we are considering the possibility of statistical significance in both directions (left and right tail). The correct answers to the statements are:

• Rejecting a 1-tailed test does not imply that you would fail to reject the corresponding 2-tailed test at the same α level. This statement is false because if you reject the null in a 1-tailed test, you might still reject it in a 2-tailed test provided the test statistic is in the extreme of the hypothesized direction.
• Rejecting a 1-tailed test implies that you would also reject the corresponding 2-tailed test at the same significance level. This statement is true because if the test statistic is extreme enough to reject the null hypothesis for a 1-tailed test, it would also be extreme enough for a 2-tailed test.
• Failing to reject a 2-tailed test implies that you would also fail to reject the corresponding 1-tailed test at the same significance level. This statement is true, as the 1-tailed test is less stringent.
• Rejecting a 2-tailed test implies that you would also reject the corresponding 1-tailed test at the same significance level. This statement is true for the same reason as the second statement.
• Failing to reject a 2-tailed test means that you will reject the corresponding single-tailed test at the same α level. This statement is false because a 2-tailed test is more stringent, so failing to reject there doesn't automatically mean you would reject using a 1-tailed test.
• Failing to reject a 1-tailed test implies that you would fail to reject the corresponding 2-tailed test at the same alpha level. This statement is true because, again, the 2-tailed test is more stringent.