20 students, a score of 10 indicates depression, a score of 0 indicates no depression, variation is unknown, but sample of 20 has a mean score of 4.4, unbiased estimate of population variance is 15. What is the variance of the distribution of means?
To find the variance of the distribution of means, we need to calculate the standard deviation first. The standard deviation of the distribution of means is also known as the standard error.
Given that the sample size is 20, the mean score is 4.4, and the unbiased estimate of the population variance is 15, we can calculate the standard error using the formula:
Standard error = √(population variance / sample size)
Let's plug in the values:
Standard error = √(15 / 20)
= √(0.75)
≈ 0.866
Now, to find the variance of the distribution of means, we square the standard error:
Variance of the distribution of means = (Standard error)^2
= 0.866^2
≈ 0.75
Therefore, the variance of the distribution of means is approximately 0.75.