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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.
Case context: A researcher conducts a pretest-posttest study with participants to evaluate a calorie-estimation training program. For each participant, they estimate the calories in a cookie before and after the training. Subtracting the pretest estimates from the posttest estimates yields a mean difference () of and a standard deviation () of . Using a dependent-samples -test, the researcher computes a score of . For a one-tailed test with degrees of freedom (), the critical value is . The corresponding -value is .
Question: 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.
Sample answer: The researcher should fail to reject the null hypothesis. The calculated score of is less than the critical value of , and the -value of is greater than the standard alpha level. This indicates that the training program does not significantly increase calorie estimates; thus, there is no statistically significant evidence that the training program was effective in this sample.
Key points:
- The decision is to fail to reject the null hypothesis.
- The calculated score () is less than the critical value (), or the -value () is greater than the alpha level.
- The training program does not significantly increase calorie estimates.
Rubric: The response must: 1. Correctly state the decision to fail to reject the null hypothesis (or retain it). 2. Justify this decision by comparing the calculated score () to the critical value () or the -value () to the alpha level (). 3. Explicitly conclude that the training program does not significantly increase calorie estimates (the program is not shown to be effective).
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Research Methods in Psychology - 4th American Edition @ KPU
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In the calorie-estimation pretest-posttest example, what is the computed score for the dependent-samples -test?
In a dependent-samples -test, a researcher fails to reject the null hypothesis when the computed 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 -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 score () to the critical value (). Because the calculated 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 -test with degrees of freedom?
Explain how a dependent-samples -test reduces pretest and posttest scores to a single set of difference scores. In your explanation, describe what a hypothetical population mean of 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 () of the difference scores is with a mean () of . If the standard deviation had been much smaller (e.g., ) while the mean difference () and sample size () remained the same, analyze how this change would affect the standard error, the computed score, and the final hypothesis decision.