Question

a certain polling agency asked 259 adult men the question: \if there was an opportunity to transform into a woman for a month, would you like to do it?\ among the respondents, 26% replied that they would want to experience the life of a woman and would use the opportunity. part: 0 / 2 part 1 of 2 calculate the margin of error for this survey. round the percentage to one decimal place. do not round intermediate steps. if 26% of 259 respondents replied that they would use the opportunity, the margin of error is %.

Explanation:

Step1: Recall the formula for margin of error

The formula for margin of error \(E\) for a proportion in a simple - random sample is \(E = z\sqrt{\frac{p(1 - p)}{n}}\). For a 95% confidence level, \(z\approx1.96\), \(p = 0.26\) (the proportion of respondents who said yes), and \(n=259\).

Step2: Calculate \(1 - p\)

\(1 - p=1 - 0.26 = 0.74\)

Step3: Calculate \(\frac{p(1 - p)}{n}\)

\(\frac{p(1 - p)}{n}=\frac{0.26\times0.74}{259}=\frac{0.1924}{259}\approx0.000743\)

Step4: Calculate \(\sqrt{\frac{p(1 - p)}{n}}\)

\(\sqrt{\frac{p(1 - p)}{n}}=\sqrt{0.000743}\approx0.02726\)

Step5: Calculate the margin of error \(E\)

\(E = 1.96\times0.02726\approx0.0534\)
To convert this to a percentage, we multiply by 100. \(E = 0.0534\times100 = 5.34\%\approx5.3\%\)

Answer:

\(5.3\)