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

Answer:

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

Step-by-step 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.

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

In which

z is the zscore that has a pvalue of $1 - \frac{\alpha}{2}$.

The margin of error is:

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

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%).