Question

A survey of 5,913 American adults concludes that 53% of them prefer Captain America to Ironman. Find the Margin of Error. Type your answer as a Percentage rounded to 1 decimal.

Answer 1

1.3%

Explanation:

Phat = 0.53

1 - phat = 1 - 0.53 = 0.47

Sample size, n = 5913

Assume the confidence level = 95%

Zcritical at 95% = 1.96

Margin of Error = Zcritical * √(phat(1 -phat)) / n

Margin of error :

1.96 * √((0.53 * 0.47) / 5913)

1.96 * 0.0064905

= 0.0127215

= 0.0127215 * 100%

= 1.272%

= 1.3%