Question

1.

a) Calculate the 95% margin of error in estimating a population mean μ for the following values. (Round your answer to three decimal places.)

n = 8,000, s² = 64

b) Consider that for s² = 64 and sample sizes of 50, 100, and 500 the margins of error are 2.217, 1.568, and 0.701 respectively. Comment on how an increased sample size affects the margin of error.

-As the sample size increases the margin of error also increases.

-As the sample size increases the margin of error decreases.    

-As the sample size increases the margin of error remains relatively constant.

Answer 1

Solution :

Given that,

sample standard deviation = s = 8

sample size = n = 8000

Degrees of freedom = df = n - 1 = 7999

a)

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,7999 = 1.960

Margin of error = E = t_/2,df * (s /n)

= 1.960 * (8 / 8000)

= 0.175

b)

From given information,

As the sample size increases the margin of error decreases.