A sample is chosen from a population with y = 46, and a treatment is then administered to the sample. After treatment, the sample mean is M = 47 with a sample variance of s2 = 16. Based on this information, what is the value of Cohen's d?
Question
Answer:
To calculate Cohen's d, we need the population mean, the sample mean, and the pooled standard deviation.Given:
Population mean:
Sample mean:
Sample variance:
To calculate the pooled standard deviation, we can use the formula:
where
Since we only have information for one sample, we can use the sample variance as an estimate for the population variance:
Substituting the given values in the formula, we have:
where
Therefore, the pooled standard deviation is equal to the sample standard deviation:
Now we can calculate Cohen's d, which is the difference between the sample mean and the population mean, divided by the pooled standard deviation:
Answer: The value of Cohen's d is 0.25.
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