When evaluating the results of a correlation test against a pre-set alpha level of $0.05$, what is the correct statistical decision if the computed $p$-value is less than or equal to $0.05$?

If the computed $p$-value for a correlation test is greater than the pre-set alpha level of $0.05$, the researcher should reject the null hypothesis.

A psychologist is evaluating the results of four different Pearson correlation tests using a standard significance level ($\alpha$) of $0.05$. Match each obtained $p$-value to the correct statistical decision and interpretation.

A researcher is evaluating the results of four separate correlation tests using a standard alpha level of $0.05$. Arrange the following obtained $p$-values in order from the result that provides the strongest evidence against the null hypothesis to the result that provides the weakest evidence against the null hypothesis.

A psychologist is designing an automated data-reporting script for a research lab to evaluate the results of multiple correlation tests. To ensure the script correctly identifies statistically significant results using a standard alpha level ($\alpha$) of $0.05$, which of the following logic frameworks should the researcher construct for the script's decision-making algorithm?

If the software output for a correlation test displays a computed $p$-value of $0.08$, the researcher should reject the null hypothesis assuming a pre-set alpha level of $0.05$.

A psychologist is investigating the relationship between social support and psychological resilience. Arrange the steps of the statistical decision-making process to correctly reflect how a researcher analyzes a $p$-value to reach a conclusion about a correlation.

A researcher conducting a study on the correlation between social media use and attention span obtains the following computed $p$-values. Match each result to the correct statistical conclusion, assuming a pre-set alpha level of $0.05$.

When evaluating the software output of a correlation test against a pre-set alpha level, what is the appropriate statistical decision if the computed $p$-value is greater than $0.05$?

A researcher finds a correlation between sleep quality and cognitive performance with a computed $p$-value of $0.035$. When evaluating this result using a standard alpha ($\alpha$) level of $0.05$, the researcher rejects the null hypothesis. However, if the researcher were to evaluate this same result using a more stringent alpha level of $0.01$, they would be required to _____ the null hypothesis.

A researcher studying the correlation between job satisfaction and productivity obtains a computed $p$-value of $0.06$. If the researcher decides to reject the null hypothesis at a pre-set alpha level of $0.05$, this statistical decision is _____.

Explain the decision rules a researcher uses when evaluating a computed $p$-value from a correlation test against a pre-set alpha level of $0.05$. In your explanation, specify the two possible outcomes and how each affects the decision regarding the null hypothesis.

Assuming the researcher has set the significance level ($\alpha$) at $0.05$, what statistical decision should they make regarding the null hypothesis, and what conclusion should they draw about the relationship between physical activity and sleep quality? Justify your decision.

Suppose a researcher studying the correlation between two psychological variables obtains a computed $p$-value of $0.055$. Explain why this specific value leads to a different decision about the null hypothesis compared to a computed $p$-value of $0.050$, referencing the significance threshold.