In the correlation study examining calorie estimates and weight ($n = 22$), what p-value did the statistical software report for Pearson's $r = -.21$?

In the calorie-estimate and weight correlation study, a two-tailed test was chosen because the researcher predicted that weight would be positively associated with calorie estimates.

Match each element from the calorie-estimate and weight correlation hypothesis test to its correct description or role in the statistical decision-making process.

In the calorie-estimate and weight study, analyzing the hand-calculated test results shows that the null hypothesis must be retained because the absolute value of the sample correlation coefficient ($.21$) is _____ than the critical value ($.444$).

Order the steps taken to evaluate the correlation coefficient by hand and determine whether to reject or retain the null hypothesis.

According to the calorie-estimate and weight study, what is the critical value for the hand-calculated correlation test with $20$ degrees of freedom?

In the context of the study investigating the correlation between calorie estimates and weight, explain the statistical logic behind why a researcher can use either the software-provided $p$-value or a hand-calculated critical value comparison to make a decision about the null hypothesis. Describe how the sample values from this study are evaluated under both methods.

Based on this new research design, calculate the degrees of freedom for the correlation test. Then, identify whether the psychologist should use a one-tailed or two-tailed test, and state the mathematical decision rule she would use if she conducts the test by hand with a critical value.

In the calorie-estimate and weight study ($N = 22$), Pearson's $r$ was calculated as $-.21$. Analyze why the researcher compared the absolute value of the correlation coefficient ($.21$) rather than the raw value ($-.21$) to the critical value ($.444$) when determining significance.