Question

1. 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? a. 0.031 b. 0.060 c. 0.063 d. 0.050 e. it’s impossible to answer this question.

Explanation:

Step1: Recall the formula for margin of error for proportion

The formula for margin of error \(E = z\sqrt{\frac{p(1 - p)}{n}}\). For a \(95\%\) confidence interval (a common - default if not specified), \(z = 1.96\), \(p=0.62\), and \(n = 250\).

Step2: Calculate \(1 - p\)

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

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

\(\frac{p(1 - p)}{n}=\frac{0.62\times0.38}{250}=\frac{0.2356}{250}=0.0009424\)

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

\(\sqrt{\frac{p(1 - p)}{n}}=\sqrt{0.0009424}\approx0.0307\)

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

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

Answer:

B. \(0.060\)