In the calorie-estimation pretest-posttest example, what is the computed $t$ score for the dependent-samples $t$-test?

In a dependent-samples $t$-test, a researcher fails to reject the null hypothesis when the computed $t$ score is less extreme than the critical value, indicating the result is not statistically significant.

Match each value or outcome from the calorie-estimation dependent-samples $t$-test example to its correct role or interpretation in the analysis.

In the provided example, the researcher evaluates the effectiveness of the training program by comparing the computed $t$ score ($1.11$) to the critical value ($1.833$). Because the calculated $t$ score is less extreme than the critical value, the researcher fails to reject the _____ hypothesis.

Order the steps a researcher must perform and evaluate to determine if the calorie-estimation training program is statistically significant, from the initial calculation of difference scores to the final hypothesis decision.

In the provided pretest-posttest study evaluating the training program, what is the critical value for the one-tailed dependent-samples $t$-test with $9$ degrees of freedom?

Explain how a dependent-samples $t$-test reduces pretest and posttest scores to a single set of difference scores. In your explanation, describe what a hypothetical population mean of $0$ represents in the context of evaluating the effectiveness of the training program.

Based on the provided statistical results, decide whether the researcher should reject or fail to reject the null hypothesis, and justify what this decision means regarding the effectiveness of the training program.

In the calorie-estimation study, the standard deviation ($SD$) of the difference scores is $24.27$ with a mean ($M$) of $8.50$. If the standard deviation had been much smaller (e.g., $5.00$) while the mean difference ($M = 8.50$) and sample size ($N = 10$) remained the same, analyze how this change would affect the standard error, the computed $t$ score, and the final hypothesis decision.