Question

If n=41n=41, ¯x=44.4x¯=44.4, and s=7.4s=7.4, find the margin of error at a 99% confidence level

Give your answer to two decimal places.

Answer 1

Solution :

Given that,

= 44.4

s = 7.4

n = 41

Degrees of freedom = df = n - 1 = 41 - 1 = 40

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

_{t /2  df} = t_0.005,40 = 2.704

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

= 2.704 * (7.4 / 41)

= 3.12

Margin of error = 3.12