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The Federal Bureau of Labor Statistics surveyed 50,000 and found the unemployment rate to be 5.8%. The margin of error was 0.2%. Construct a confidence interval for the unemployment rate.

User Rafay Khan
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3 votes

Answer:

The confidence interval for the unemployment rate is (0.056, 0.06) = (5.6%, 6%).

Explanation:

In a sample with a number n of people surveyed with a probability of a success of
\pi, and a confidence level of
1-\alpha, we have the following confidence interval of proportions.


\pi \pm z\sqrt{(\pi(1-\pi))/(n)}

In which

z is the zscore that has a pvalue of
1 - (\alpha)/(2).

The margin of error is:


M = z\sqrt{(\pi(1-\pi))/(n)}

The lower bound of the interval is:


\pi - M

The upper bound of the interval is:


\pi + M

In this problem, we have that:


\pi = 0.058, M = 0.002

So


\pi - M = 0.058 - 0.002 = 0.056


\pi + M = 0.058 + 0.002 = 0.06

The confidence interval for the unemployment rate is (0.056, 0.06) = (5.6%, 6%).

User AnsellC
by
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