In a recent poll, 490 people were asked if they liked dogs, and 75% said they did. Find the Margin of Error for this poll, at the 90% confidence level.

Question

In a recent poll, 490 people were asked if they liked dogs, and 75% said they did. Find the Margin of Error for this poll, at the 90% confidence level. Give your answer to four decimal places if possible.

Answer 1

margin of error = z-critical for 90% confidence level * standard error

sample proportion = 0.75 (phat)

sample size = 490 (n)

standard error = sqrt(0.75*0.28/490) = 0.0195615

z-critical for 90% CL = z-score for 0.95 probability =1.65

margin of error = 1.65 * 0.0195615= 0.032276

Which is to 4dp=0.0323