Question

a survey of 850 people reported that 42% favored the re - election of the current governor. find the margin of error. % question 2 2 pts a survey of 850 people reported that 42% favored the re - election of the current governor. find the upper bound of the confidence interval. %

Explanation:

Step1: Find the margin of error formula

The formula for margin of error \(E\) for a proportion is \(E = z\sqrt{\frac{p(1 - p)}{n}}\). For a 95% confidence interval (common in surveys if not specified otherwise), \(z = 1.96\), \(p=0.42\), \(n = 850\).

Step2: Calculate \(1-p\)

\(1 - p=1 - 0.42=0.58\)

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

\(\frac{0.42\times0.58}{850}=\frac{0.2436}{850}\approx0.0002866\)

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

\(\sqrt{0.0002866}\approx0.01693\)

Step5: Calculate \(E\)

\(E = 1.96\times0.01693\approx0.0332\) or \(3.32\%\)

Step6: Find the upper - bound of the confidence interval

The confidence interval for a proportion is \(\hat{p}-E

Answer:

Margin of error: \(3.32\%\)
Upper - bound of the confidence interval: \(45.32\%\)