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Analyze the relationship between the sample size () and the degrees of freedom () in this one-sample -test. How would an increase in sample size affect the degrees of freedom and the critical value needed to reject the null hypothesis?
Question: Analyze the relationship between the sample size () and the degrees of freedom () in this one-sample -test. How would an increase in sample size affect the degrees of freedom and the critical value needed to reject the null hypothesis?
Sample answer: In a one-sample -test, degrees of freedom are calculated as , which is when . Increasing the sample size would increase the degrees of freedom, which generally leads to a less extreme (smaller absolute) critical value, making it easier to reject the null hypothesis for a given effect size.
Key points:
- Degrees of freedom are defined as , representing 9 in this study.
- Increasing sample size directly increases the degrees of freedom.
- Larger degrees of freedom result in less extreme critical values (closer to zero).
Rubric: The answer must state that degrees of freedom are calculated as , show that increasing the sample size increases degrees of freedom, and explain that higher degrees of freedom result in a lower/less extreme critical value.
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Research Methods in Psychology - 4th American Edition @ KPU
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