Which of the following statements is (are) true regarding 1-tailed and 2-tailed

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 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 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

Explanation / Answer

P-value of the two tailed test is greater than p-value of one tailed test. And we will reject the null hypothesis when p-value is less than   level. If p-value of one tailed test is less than , it is not necessary that p-value of two tailed will be greater than .

Cannot conclude that "Rejecting a 1 tailed test implies that you would fail to reject the corresponding 2 tailed test at the same level".

Cannot conclude that "Rejecting a 1-tailed test implies that you would also reject the corresponding 2-tailed test at the same significance level"

Cannot conclude that "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"

Cannot conclude that "Failing to reject a 2-tailed test means that you will reject the corresponding single tailed test at the same level"

Correct options:

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 1-tailed test implies that you would fail to reject the corresponding 2-tailed test at the same alpha level.

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