Question

If n=500 and ˆ p p ^ (p-hat) =0.45, find the margin of error at a 90% confidence level. Give your answer to three decimals.

Answer 1

solution

Point estimate = sample proportion = = x / n = 0.45

1 -   = 1- 0.45 =0.55

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

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

= 1.645 *((0.45*0.55) /500 )

= 0.037