When a researcher switches from a two-tailed t-test to a one-tailed t-test (with the same degrees of freedom and significance level), the critical value for the one-tailed test is less extreme than that of the two-tailed test, making it easier to reject the null hypothesis in the predicted direction.

A researcher is considering switching from a two-tailed $t$-test (with critical values of $\pm 2.262$) to a one-tailed $t$-test because they have a strong theoretical reason to expect an underestimation of scores. What is the primary statistical consequence of this change?

A psychology researcher predicts that a new therapy will decrease patient anxiety scores. They decide to use a one-tailed $t$-test (critical value $-1.833$) instead of a two-tailed $t$-test (critical values $\pm 2.262$). Match each obtained $t$-statistic with the correct statistical outcome for this one-tailed test.

A psychology researcher predicts that a new mindfulness intervention will decrease anxiety scores. They are deciding whether to use a one-tailed test (critical value = -1.833) or a two-tailed test (critical values = ±2.262). Arrange the following scenarios in order of their statistical outcome, starting with the one that results in a rejection of the null hypothesis and ending with the one where rejection is statistically impossible.

If a researcher switches from a two-tailed $t$-test to a one-tailed $t$-test based on a predicted direction of scores, what is the statistical consequence if the actual results are in the opposite direction of that prediction?

Match each statistical scenario or characteristic with its corresponding description when a researcher decides between a one-tailed and two-tailed $t$-test.

A researcher chooses a one-tailed $t$-test ($t_{crit} = -1.833$) instead of a two-tailed test ($t_{crit} = \pm 2.262$) to test a predicted underestimation of scores. In evaluating an unexpected outcome of $t = +4.25$ (the opposite of the prediction), the researcher must judge the result to be statistically _____, confirming that their initial design choice has rendered even extreme contradictory evidence mathematically irrelevant.

A researcher predicted before data collection that participants would underestimate their daily screen time. Based on this directional hypothesis, they selected a one-tailed $t$-test with a critical value of $-1.833$. After running the study, they obtained $t = -2.05$. The researcher correctly concludes that the null hypothesis can be rejected.

A one-tailed $t$-test places the entire significance level ($\alpha$) into _____ tail(s) of the sampling distribution, which is why its critical value is less extreme than the critical values of a two-tailed test conducted at the same $\alpha$ level and degrees of freedom.

A peer reviewer is evaluating whether a researcher was scientifically justified in switching from a two-tailed $t$-test (critical values $\pm 2.262$) to a one-tailed $t$-test (critical value $-1.833$). Arrange the following steps in the order the reviewer should complete them to reach a defensible judgment.

Based on the provided statistical guidelines, describe how switching from a two-tailed $t$-test to a one-tailed $t$-test changes the critical values, the ease of rejecting the null hypothesis, and the consequence if actual results occur in the direction opposite to the researcher's prediction.

Explain why the researcher is unable to reject the null hypothesis in this scenario, and describe the trade-off of their decision to use a one-tailed test.

A researcher predicts that students will underestimate their study hours and chooses a one-tailed $t$-test with a critical value of $-1.833$ (compared to the two-tailed critical values of $\pm 2.262$). If the experiment yields a calculated $t$-statistic of $-2.05$, and a follow-up experiment yields a $t$-statistic of $+3.10$, apply the rules of one-tailed testing to determine and justify the outcome for each experiment.