Question

If the population mean is 1000

For n = 9 ,16 , 25 , 49, 100, 400 , 900, 1600, 2500, 4000, 10000

Compute the sample mean for each value

If the population standard deviation is 100

What is the sample means standard deviation

For n = 9 ,16 , 25 , 49, 100, 400 , 900, 1600, 2500, 4000, 10000

How does the variance change as we increase the sample size?

Answer 1

Solution:

Given in the question

Mean = 1000

Sample mean for every sample size is same

For sample size n= 9,16,25,49,100,400,900,1600,2500,4000,10000

Sample mean is same i.e. 1000

Population standard deviation = 100

Than n= 9, sample standard deviation = 100/Sqrt(9) = 33.33

For n= 25, sample standard deviation = 100/sqrt(25) = 20

For n= 16, sample standard deviation = 100/sqrt(16) = 25

For n= 49, sample standard deviation = 100/sqrt(49) =14.29

For n= 64, sample SD = 100/sqrt(64) = 12.5

For n= 100 sample SD = 100/sqrt(100) = 10

For n= 400, sample SD = 100/sqrt(400) = 5

For n= 900, sample SD = 100/sqrt(900) = 3.33

For n= 1600, sample SD = 100/sqrt(1600) = 2.5

For n=2500, sample SD = 100/Sqrt(2500) = 2

For n= 4000, sample SD =100/sqrt(4000) = 1.58

For n= 10000, sample SD = 100/sqrt(10000) = 1

As sample size is increasing the variance decreases and standard deviation also decreases.