a score of 10 indicates severe depression, while a score of 0 indicates no depression. From reports, she is able to find out about past testing. Fourth graders at her school usually score 5 on the scale, but the variation is not known. Her sample of 20 fiftsh graders has a mean depression score of 4.4.
The counselor calculates the unbiased estimate of the population's variance to be 15. What is the variance of the distribution of means?
Standard error of mean = Standard deviation/√(n-1)
SD^2 = Variance
Variance of mean = 4.4/19 = ?
15/19 = 0.79
To find the variance of the distribution of means, we need to use the formula for the variance of the sampling distribution.
The formula for the variance of the sampling distribution is given by:
variance of the sampling distribution = variance of the population / sample size
In this case, the variance of the population is given as 15, and the sample size is 20.
So, plugging in the values into the formula, we get:
variance of the sampling distribution = 15 / 20
= 0.75
Therefore, the variance of the distribution of means is 0.75.