Question

What is the margin of error for a random sample of 400 respondents. Assume the 95% level of confidence. Show your work.

Answer 1

Solution :

Given that,

n = 400

Point estimate = sample proportion = = 0.5 ( when estimate is not known than asume that 0.5)

1 - = 1 -0.5=0.5

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

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

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

= 1.96 (((0.5*0.5) /400 )

E =0.0490

margin of error =0.0490