Question: A population consists of the five numbers 1, 3, 5, 7 and 9. Consider all the samples of size 2 that can be drawn without replacement from the population. Find the mean and the variance of the sampling distribution means.
A ) 6 and 4.05 B ) 6 and 3 C ) 5 and 3.05 D ) 5 and 3
Steps to derive
1 There are 10 samples of size 2 that can be drawn without replacement.
2 The samples are
3 The corresponding means are
4 The mean of the sampling distribution of means is μx‾ = sum of the sample means number of sample means)
5 μx‾ = 5010 = 5
6 The variance of the sampling distribution of means is (σx‾)2 = (2-5)²+(3-5)²+...........+(8-5)²10 = 3010 = 3
7 Therefore the mean and standard deviation of the sampling distribution means are 5 and 3.
