Verizon Wireless would like to estimate the proportion of households that use cell phones for their phone service without a land line. A random sample of 150 households was selected and 48 relied strictly on cell phones for their service. The 95% confidence interval for the proportion based on this sample is ------- .
A)(0.257, 0.383)
B)(0.185, 0.456)
C)(0.223, 0.417)
D)(0.165, 0.475)

Question

Quizplus · Accepted Answer

The 95% confidence interval for the proportion can be calculated using the formula for a confidence interval for a proportion: $p \pm z*\sqrt{\frac{p(1-p)}{n}}$, where $p$ is the sample proportion, $z$ is the z-score corresponding to the confidence level (for 95%, $z = 1.96$), and $n$ is the sample size. Here, $p = \frac{48}{150} = 0.32$, so the calculation is $0.32 \pm 1.96*\sqrt{\frac{0.32(1-0.32)}{150}}$, which gives the interval (0.257, 0.383).

Verizon Wireless Would Like to Estimate the Proportion of Households