Suppose that we will take a random sample of size n from a p

Suppose that we will take a random sample of size (n) from a population having mean (m) and standard deviation (s). For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean x:

a. m =10, s=2, n=20

b. m=500, s=0.5, n=100

c. m=3, s=0.1, n=4

d. m=100, s=1, n=1,600

Solution

a) sampling distribution is Normal ( mean =10 ,and sample s.d = ( 2 /sqrt(20) ) = 0.4472136 )

b) sampling distribution is Normal ( mean = 500 and sample s.d = ( 0.5 / sqrt(100) ) = 0.05 )

c) sampling distribution is Normal ( mean = 3 and sample s.d = ( 0.1 / sqrt(4) ) = 0.05 )

d) sampling distribution is Normal ( mean = 100 and sample s.d = ( 1 / sqrt(1600) ) = 0.025 )