Question

1. If n=10, ¯ x (x-bar)=43, and s=10, find the margin of error at a 95% confidence level (use at least two decimal places)

2. If n=11, ¯x (x-bar)=35, and s=4, find the margin of error at a 99% confidence level (use at least three decimal places)

Answer 1

Solution :

Given that,

= 43

s =10

n = Degrees of freedom = df = n - 1 = 10- 1 = 9

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,9 = 2.262 ( using student t table)

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

= 2.262 * ( 10/ 10)

= 7.15

b.

= 35

s =4

Degrees of freedom = df = n - 1 =11 - 1 = 10

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005,10 = 3.169    ( using student t table)

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

=  3.169 * ( 4/ 11) = 3.822