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Based on the provided statistical results, diagnose whether the researcher should reject or retain the null hypothesis, and explain what this decision means regarding the differences between the study environments.
Case context: A research team is examining the effect of three different study environments (silent, background music, noisy) on student memory retention. After running a one-way ANOVA, they obtain a computed statistic of . They look up the critical value in an table for their degrees of freedom at an alpha level of and find it is . The lead researcher is unsure whether they should report that the study environments had a significant effect on memory retention.
Question: Based on the provided statistical results, diagnose whether the researcher should reject or retain the null hypothesis, and explain what this decision means regarding the differences between the study environments.
Sample answer: The researcher should retain the null hypothesis. Because the computed statistic of is less than the critical value of , the corresponding -value will be greater than the alpha level of . Retaining the null hypothesis means there is insufficient statistical evidence to claim that memory retention differs among the three study environments.
Key points:
- Compare the computed ratio () to the critical value () and state that it is smaller.
- Explain that the corresponding -value is greater than the alpha level of .
- State the statistical decision to retain the null hypothesis.
- Conclude that there is insufficient statistical evidence to claim the population means differ among the environments.
Rubric: Grading should be based on: 1) Correctly identifying that the computed ratio () is less than the critical value (). 2) Correctly stating that the null hypothesis must be retained because the associated -value is greater than . 3) Interpreting this statistical decision as meaning there is insufficient evidence to conclude that differences in memory retention exist among the study environments.
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Research Methods in Psychology - 4th American Edition @ KPU
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