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Explain the comprehension-level logic that allowed Kanner and colleagues to reject the null hypothesis in favor of the alternative hypothesis. How did the likelihood of obtaining their sample correlation under the assumption that the null hypothesis is true lead to their final conclusion about the population?
Case context: A student in an introductory research methods course is reviewing Kanner and colleagues' study on the relationship between daily hassles and psychological symptoms. In this study, the researchers found a sample correlation of and used the logic of null hypothesis testing to make an inference about the population.
Question: Explain the comprehension-level logic that allowed Kanner and colleagues to reject the null hypothesis in favor of the alternative hypothesis. How did the likelihood of obtaining their sample correlation under the assumption that the null hypothesis is true lead to their final conclusion about the population?
Sample answer: Kanner and colleagues started by assuming the null hypothesis was true (meaning no correlation exists in the population). Under this assumption, they evaluated how likely it would be to obtain their strong sample correlation of . Since such a strong relationship is highly unlikely to occur by chance under the null hypothesis, they concluded that the null hypothesis was an improbable explanation. Consequently, they rejected the null hypothesis and concluded that a positive correlation does exist in the population (supporting the alternative hypothesis).
Key points:
- Explain that the null hypothesis assumes no correlation in the population.
- Explain that the sample correlation () is evaluated based on its likelihood under the null hypothesis.
- State that the sample relationship was determined to be unlikely under the null hypothesis.
- Explain that this low likelihood led the researchers to reject the null hypothesis in favor of the alternative hypothesis (concluding a positive correlation exists in the population).
Rubric: The response should demonstrate comprehension of null hypothesis testing logic. It must explain that the null hypothesis is assumed true first, that the observed sample correlation () is highly unlikely under that assumption, and that this low likelihood justifies rejecting the null hypothesis to conclude that a positive correlation exists in the population.
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Research Methods in Psychology - 4th American Edition @ KPU
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