Respuesta :
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 [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
The lower bound of the interval is:
[tex]\pi - M[/tex]
The upper bound of the interval is:
[tex]\pi + M[/tex]
In this problem, we have that:
[tex]\pi = 0.058, M = 0.002[/tex]
So
[tex]\pi - M = 0.058 - 0.002 = 0.056[/tex]
[tex]\pi + M = 0.058 + 0.002 = 0.06[/tex]
The confidence interval for the unemployment rate is (0.056, 0.06) = (5.6%, 6%).
