Question

Kendall wants to estimate the percentage of vegetarians who are also vegan. She surveys 150 vegetarians and finds that 45 are vegan. Find the margin of error for the confidence interval for the population proportion with a 95% confidence level.

Answer 1

0.0733364

Explanation:

Given :

Number of vegans = x ;

Sample size, n = 150

Zα/2 ; Zcritical at 95% = 1.96

p = x / n = 45 / 150 = 0.3

Margin of Error :

Zcritical * √(p(1 - p) / n)

1.96 * √(0.3(1 - 0.3) / 150)

Margin of Error :

1.96 * √(0.3 * 0.7) / 150)

1.96 * √0.0014

Margin of Error = 0.0733364