In the context of a $t$-test, what is the appropriate statistical decision if the obtained $p$-value is less than or equal to the standard alpha level of .05?

A researcher conducts a $t$-test and calculates a $p$-value of .08. Assuming a standard alpha level of .05, the researcher should reject the null hypothesis and conclude that a significant difference exists.

Match each statistical value or threshold with the corresponding decision or role in the process of evaluating a $t$-test result.

A researcher conducts a $t$-test and obtains a $p$-value of .02. With the alpha level set at .05, arrange the following steps in the correct logical sequence to evaluate the result and conclude the study.

When a t-test yields a p-value greater than .05, this result proves that the null hypothesis is true and that no real difference exists between the groups.

A researcher investigating the effect of exercise on mood finds a $p$-value of .03 in their $t$-test results. Arrange the following steps in the correct logical sequence to analyze this $p$-value and reach a final statistical conclusion using a standard alpha level of $\alpha = .05$.

A research team is evaluating the results of four independent $t$-tests investigating various psychological factors in student performance. Match each study's obtained $p$-value to its correct statistical decision and conclusion, using a standard alpha level of $\alpha = .05$.

When evaluating the output of a $t$-test, what is the appropriate conclusion if the obtained $p$-value is less than or equal to the typical alpha level of .05?

A researcher conducting a study on the efficacy of a new therapy obtains a $p$-value of .05 from an independent samples $t$-test. The researcher decides to retain the null hypothesis, claiming that the evidence is not strong enough to be certain of a difference. When evaluating the validity of this conclusion against the standard alpha level of $\alpha = .05$, a peer reviewer would judge the conclusion as invalid because the researcher was technically obligated to _____ the null hypothesis.

A researcher obtains a $p$-value of .05 and concludes that a significant difference exists. A reviewer argues that the researcher should have retained the null hypothesis because .05 is not strictly less than the alpha level of .05. According to the conventional decision rule for statistical significance, the reviewer's argument is _____.

State the standard decision rules for evaluating a $p$-value obtained from a $t$-test when comparing it to a typical alpha level of $\alpha = .05$. Specify the actions taken regarding the null hypothesis and the conclusions drawn for both possible outcomes.

Explain how the researcher should interpret this $p$-value of .03 relative to their alpha level, detailing the appropriate decision regarding the null hypothesis and what this decision means for the effectiveness of the new study technique.

A study investigating the effect of background music on concentration levels obtains a $p$-value of .15 from a $t$-test. Apply the standard statistical criteria ($\alpha = .05$) to determine the decision about the null hypothesis and state the final conclusion.