One-Tailed Test

Example of a Two-Tailed Test

A researcher is exploring whether a new background noise level changes the time it takes for participants to complete a puzzle. Because they are unsure if the noise will make participants faster or slower, they choose to use a Two-Tailed Test. Based on this choice, when will the researcher reject the null hypothesis?

A clinical psychologist is conducting a study to see if a new mindfulness exercise changes the average number of hours patients sleep per night. They expect a difference but do not know if sleep will increase or decrease, so they opt for a two-tailed test. Arrange the following steps of their hypothesis testing process in the correct chronological order.

A psychology researcher is analyzing the effects of a new therapy on anxiety scores using a two-tailed test. Match each statistical component with the description that accurately analyzes its functional role in the structure of this non-directional hypothesis test.

A psychologist evaluating the efficacy of a new antidepressant uses a two-tailed test. Although they expect the drug to reduce symptoms, they justify the two-tailed approach as being more scientifically rigorous because it allows for the statistical detection of an unexpected increase in symptoms. This justification is methodologically sound because, at a fixed significance level of $\alpha = 0.05$, the two-tailed test requires a more extreme result to justify rejecting the null hypothesis in the predicted direction than a test that only considers a single tail of the distribution.

In the context of hypothesis testing, how many distinct critical values are typically utilized to establish the rejection regions for a two-tailed test?

A researcher should only use a two-tailed test if they have a strong theoretical justification for predicting that the experimental results will be significantly higher than the hypothesized population mean.

An approach to hypothesis testing where researchers reject the null hypothesis if their calculated test statistic falls into the extreme regions of either the positive or negative tail of the distribution is called a _____ test.

A clinical psychologist is evaluating whether a new mindfulness training program changes the average duration of deep sleep in adults. Since they do not have a strong prediction regarding the direction of the change, they conduct a two-tailed test with an alpha level of $\alpha = 0.05$, which yields critical values of $-1.96$ and $+1.96$. After collecting and analyzing data, the psychologist obtains a test statistic of $z = -2.10$. Because this statistic falls into the negative tail, the psychologist should ____ the null hypothesis.

A psychologist is analyzing the results of an experiment on a new anxiety-reduction therapy. They decide to use a two-tailed t-test with a significance level of $\alpha = 0.05$. During their analysis, they compare the structure of their chosen test to a hypothetical one-tailed test with the same $\alpha = 0.05$ that assumes the therapy will reduce anxiety. Which of the following statements accurately analyzes the relationships, critical boundaries, and error rates of these two testing approaches?

Match each researcher's justification for their choice of a two-tailed test with the most appropriate methodological evaluation of that decision.