Question

What is the margin of error for a confidence interval with the following properties: s = 106.3, n = 50, α = 0.05?

How large would the sample size need to be for the confidence interval to have a margin of error of 10?

Answer 1

Solution :

Given that,

sample standard deviation = s = 106.3

sample size = n = 50

Degrees of freedom = df = n - 1 = 50 - 1 = 49

= 0.05

/2 = 0.025

t/2,df = t_0.025,49 = 2.010

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

= 2.010 * (106.3 / 50)

Margin of error = E = 30.22

2) margin of error = E = 10

sample size = n = [t/2,df* s / E]²

n = [2.010 * 106.3 / 10 ]²

n = 456.51

Sample size = n = 457