Question

question 10
1 pts
a random sample of 250 sports fans are surveyed, and 62% of these surveyed fans say that football is their favorite sport. if the goal is to use this sample data to construct a confidence interval, what will the margin of error be?
0.031
0.060
0.063
0.050
its impossible to answer this question.

Explanation:

Step1: Determine the formula for margin of error

For a proportion, the margin of error \(E = z\sqrt{\frac{p(1 - p)}{n}}\). When the confidence level is not given, we assume a \(95\%\) confidence level. For a \(95\%\) confidence level, \(z = 1.96\). Here \(p=0.62\) and \(n = 250\).

Step2: Calculate \(1 - p\)

\(1-p=1 - 0.62=0.38\)

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

\(\frac{0.62\times0.38}{250}=\frac{0.2356}{250}=0.0009424\)

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

\(\sqrt{0.0009424}\approx0.0307\)

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

\(E=1.96\times0.0307\approx0.060\)

Answer:

\(0.060\)