Question

SELF ASSESSMENT A population has mean 75 and standard deviation 12. a. Random samples of size 121 are taken. Find the mean and standard deviation of the sample mean. b. How would the answers to part (a) change if the size of the samples were 400 instead of 121?

Answer 1

X ~ N ( µ = 75 , σ = 12 )

Part a)

Mean of the sample mean µ_X̅ = µ = 75

Standard deviation of sample mean σ_X̅ = σ / √ (n) = 12/√121 = 1.0909

Part b)

Mean of the sample mean µ_X̅ = µ = 75

Standard deviation of sample mean σ_X̅ = σ / √ (n) = 12/√400 = 0.6

As the sample size increase mean remain same, but standard deviation of the sample mean decreases.