According to the logic of null hypothesis testing, what decision is typically made when researchers find a sample result that is fairly likely to occur even if there were no true difference in the population?

Based on the logic of null hypothesis testing, match each research scenario with the appropriate conclusion or decision researchers would reach.

Suppose a study finds a strong correlation of $r = +.72$ between mindfulness practice and stress reduction. If the researcher determines that this result is highly unlikely to occur if no true relationship existed in the population, the logic of null hypothesis testing dictates that they should ________ the null hypothesis.

Suppose a study finds a strong correlation of $r = +0.60$ between daily hassles and stress symptoms. If the researchers analyze this result as being 'fairly likely' to occur by chance and subsequently decide to reject the null hypothesis, their logic is consistent with standard null hypothesis testing procedures.

A researcher finds a weak correlation of $r = +0.08$ between herbal tea consumption and exam scores. Arrange the steps of the logical evaluation process they should use to justify the decision to retain the null hypothesis.

Imagine you are constructing a new research scenario for a textbook to illustrate the correct logic for rejecting a null hypothesis. Which of the following combinations of findings and justifications should you assemble to provide a scientifically sound example?

According to the logic of null hypothesis testing, if researchers find a very small difference in talkativeness between men and women ($d = 0.06$), they should reject the null hypothesis.

Arrange the steps in the correct logical order that researchers follow when applying null hypothesis testing to a strong sample correlation ($r = +.60$).

Analyze the logic of null hypothesis testing by matching each research scenario or probability condition with the correct statistical decision and rationale.

A researcher observes a very small difference in talkativeness between men and women ($d = 0.06$) and decides to reject the null hypothesis. Evaluating this research decision based on null hypothesis testing logic, this decision is incorrect because a difference this small is _____ even if there were no true difference in the population, meaning the null hypothesis should have been retained.

Recall the two examples of null hypothesis testing decisions described in the text. For each example, state the variables studied, the specific statistical value ($d$ or $r$) reported, the likelihood of the result if the null hypothesis were true, and the final decision made regarding the null hypothesis.

Based on the logic of null hypothesis testing, what decision should the psychologists make regarding the null hypothesis? Explain the reasoning behind this decision in terms of the likelihood of the sample result when there is no true difference in the population.

Imagine you find a strong correlation of $r = +.65$ between mindfulness practice and test anxiety. If you determine this sample relationship is highly unlikely to occur if the null hypothesis were true, apply the logic of null hypothesis testing to state your statistical decision and your conclusion about the population relationship.