A random sample of 10 independent observations from a normally distributed population yielded the following values 51, 53, 49, 43, 47, 46, 45, 30, 60, 52.

Question

a) Estimate the standard deviation of the sampling distribution of means for samples like this one.

b) Using á = .05, test the hypothesis that the true mean is 50 against the alternative that the true mean is not 50.

c) State the conclusion.

Answer 1

a) Find the mean first = sum of scores/number of scores

Subtract each of the scores from the mean and square each difference. Find the sum of these squares. Divide that by the number of scores to get variance.

Standard deviation = square root of variance

Standard deviation of the sampling distribution of means = SEm = SD/√n

b) Z = (mean1 - mean2)/standard error (SE) of difference between means

SEdiff = √(SEmean1^2 + SEmean2^2)

SEm = SD/√n

If only one SD is provided, you can use just that to determine SEdiff.

Find table in the back of your statistics text labeled something like "areas under normal distribution" to find the proportion/probability related to the Z score.

c) Depends on your calculations.