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.