SOLUTION: A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. In the general population the number of such d

Question 1136578: A psychologist is interested in the conditions that affect the number of dreams per month that people report in which they are alone. In the general population the number of such dreams per month follows a normal curve, with μ = 5 and σ = 4. The psychologist studies 36 individuals and found that their mean number of alone dreams is 8. What is the Z score for this groups mean in the distribution of sample means?

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Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
the sample is of 36 individuals.
the mean of the population is 5 and the standard deviation of the population is 4.
the mean of the sample is 8.

the standard error of the sample is the standard deviation of the population divided by the square root of the sample size.

that is equal to 4 / sqrt(36) = 4/6 = 2/3 = .3333.....

by definition, the standard error of the sample is the standard deviation of sample means taken from a large number of samples whose size equals 36.

the z-score for the sample is (x - m) / s.

z is the sample mean.
m is the population mean.
s is the standard error of the sample.

the z-score becomes equal to (8 - 5) / (2/3) = 3 / (2/3) = 4.5.

here's a reference on distribution of sample means.

http://davidmlane.com/hyperstat/A13660.html

the average of all the sample means approaches the population mean.

the standard deviation of the distribution of all the sample means is roughly equal to the standard deviation of the population divided by the sample size.

the larger the sample size, the smaller the standard deviation of the sample means.

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