Question

1. If n=240 and ˆp (p-hat) =0.3, find the margin of error at a 90% confidence level

Give your answer to three decimals.

2. In a recent poll, 160 people were asked if they liked dogs, and 61% said they did. Find the margin of error of this poll, at the 90% confidence level.

Give your answer to three decimals

Answer 1

We know that-

Margin of error E = Z_c * sqrt[( p^ * ( 1 - p^))/n]

1. We have given n = 240 , p^ = 0.3 , C = 0.90

Therefore Margin of error = E = Z_0.90 * sqrt[ (0.3 * (1 - 0.3)) / 240]

= 1.645 * sqrt(0.000875)

= 1.645 * 0.02958

= 0.049

Margin of error E = 0.049

2. Here n = 160 , p^ = 0.61 and C = 90

Therefore Margin of error = E = Z_0.90 * sqrt[ (0.61 * (1 - 0.61))/ 160]

= 1.645 * sqrt(0.001487)

= 1.645 * 0.03856

= 0.063

Margin of error E = 0.063

Hope this will help you. Thank you :)