Question

If n=410 and ˆpp^ (p-hat) =0.41, find the margin of error at a 95% confidence level

Give your answer to three decimals

Answer 1

Solution :

Given that,

n = 410

Point estimate = sample proportion = = 0.41

1 -   = 1- 0.41 =0.59

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E = Z/2    * ((( * (1 - )) / n)

= 1.96 (((0.41*0.59) / 410)

E= 0.047

Margin of error = E =0.047