Question

one day, a poll appeared on a certain website. it asked \do you believe that rain can soothe the heart and cleanse the mind?\ unsurprisingly, 30% of 481 answers were \yes\. calculate the margin of error for this poll. round the percentage to one decimal place. do not round intermediate steps. if 481 people were asked that question and 30% of them replied \yes\, the margin of error is
%

Explanation:

Step1: Identify the formula for margin of error

The formula for margin of error (ME) for a proportion is \(ME = z\sqrt{\frac{p(1 - p)}{n}}\). For a simple - case (assuming a 95% confidence level, \(z\approx1.96\)), \(p = 0.3\) (the proportion of "Yes" answers), and \(n=481\) (the sample size).

Step2: Calculate \(p(1 - p)\)

$$p(1 - p)=0.3\times(1 - 0.3)=0.3\times0.7 = 0.21$$

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

$$\frac{p(1 - p)}{n}=\frac{0.21}{481}\approx0.0004366$$

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

$$\sqrt{\frac{0.21}{481}}\approx\sqrt{0.0004366}\approx0.0209$$

Step5: Calculate the margin of error

$$ME = 1.96\times0.0209\approx0.041$$

To convert this to a percentage, we multiply by 100. So \(ME = 4.1\%\)

Answer:

\(4.1\)