Question: Assume that the weights of 3,000 students at a university are normally distributed with mean 150 pounds and a standard deviation of 7 pounds. If 100 samples of 30 students each are obtained, then what would be the expected mean and standard deviation of the resulting sampling distribution of means if sampling were done without replacement?
A ) 150 lbs, 73000 lbs B ) 150 lbs, 710 lbs C ) 150 lbs, 730 lbs D ) 150 lbs, 1.272 lbs
Steps to derive
1 Here the distribution of sample means will be approximately normal with a mean of 150 lbs.
2 The standard deviation of the sample means is given by (σn)×N-nN-1 the correction factor being [N-nN-1] applied to the standard error where n is the size of the sample and N is the size of the finite population.
3 The standard deviation of the sample means = (σn)×N-nN-1 = (730)×3000-303000-1 = 1.278 × 0.99515 = 1.272 lbs
