Question

Find the margin of error for a​ 95% confidence interval for estimating the population mean when the sample standard deviation equals 100​, with a sample size of​ (i) 484 and​ (ii) 1521. What is the effect of the sample​ size? ​(i) Find the margin of error for a​ 95% confidence interval for estimating the population mean when the sample standard deviation equals 100 with a sample size of 484.

Answer 1

i) the margin of error for a​ 95% confidence interval for estimating the population mean is

M.E = 8.909

ii) the margin of error for a​ 95% confidence interval for estimating the population mean is

M.E = 5.025

Explanation:

Step:-(i)

i ) Given sample size n = 484

Given sample standard deviation 'S' = 100

Margin of error for 95% confidence interval for estimating the population mean is determined by

`M.E = (1.96 X 100)/(√(484) ) = 8.909`

ii) Given sample size n =1521

Given sample standard deviation 'S' = 100

Margin of error for 95% confidence interval for estimating the population mean is determined by

`M.E = (1.96 X 100)/(√(1521) ) = 5.025`