Question

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.

Answer 1

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%).