An Internet service provider sampled 540 customers and found that 55 of them experienced an interruption in their service during the previous month. Construct a 95% confidence interval for the Proportion of all customers who have experienced a service interruption.
A) (0.076, 0.127)
B) (0.873, 0.924)
C) (0.102, 0.898)
D) (0.080, 0.123)

Question

Quizplus · Accepted Answer

The confidence interval for a proportion can be calculated using the formula $p \pm z\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (1.96 for 95%), and $n$ is the sample size. Here, $p = \frac{55}{540}$, $n = 540$, and $z = 1.96$. Plugging these values into the formula gives a confidence interval of approximately (0.076, 0.127).

An Internet Service Provider Sampled 540 Customers and Found That