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Based on the researcher's goal to estimate population variability, decide which denominator they should use and explain what would happen to the estimate if they used the other denominator.
Case context: A social psychologist is studying social media usage and measures the daily screen time (in minutes) of a sample of 30 college students. The researcher intends to use this sample to estimate the standard deviation of daily screen time for the entire college student population. They are debating whether to use (30) or (29) in the denominator of their standard deviation calculation.
Question: Based on the researcher's goal to estimate population variability, decide which denominator they should use and explain what would happen to the estimate if they used the other denominator.
Sample answer: The researcher should use (which is 29) because they are estimating the variability of the larger population from a sample. If they used (30) instead, the resulting standard deviation would underestimate the true variability of the population. This is because sample standard deviations naturally tend to be lower than the population standard deviations, and dividing by fails to correct for this underestimation.
Key points:
- Identify (29) as the appropriate denominator for estimating population variability.
- Explain that sample standard deviation naturally underestimates the true population standard deviation.
- Describe how dividing by (30) leads to an underestimated (biased) value of population variability.
- Explain how the correction increases the value to make it a more accurate estimate.
Rubric: The student must choose the denominator (29) and explain that using the uncorrected denominator (30) would underestimate the true population standard deviation due to the sample's natural tendency to have lower variability.
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Research Methods in Psychology - 4th American Edition @ KPU
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