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Question

the mean of a population of 300000000is 80 the standard deviation is 15 if samples are taken what is the standard deviation of the means of samples:

a. of size 10

b. of size 50

c. of size 200

d. of size 1000

Answer 1

Wal can't be right. The standard deviation of the means of samples is always lower than the standard deviation of the population. The formula is

s / sqrt(n)

where s is the standard deviation of the population.

for a), your answer is 15 / sqrt(10)

Answer 2

Sample sd = √(n/(n-1)) * σ

a) size 10

Sample sd
= √(10/(9)) * 15
≈15.81

b) size 50

Sample sd
= √(50/(49)) * 15
≈15.15

a) size 200

Sample sd
= √(200/(199)) * 15
≈15.04

a) size 1000

Sample sd
= √(1000/(999)) * 15
≈15.01