In a sample of 25 iPhones, 12 had over 85 apps downloaded. Construct a 90% confidence interval for the population proportion of all iPhones that obtain over 85 apps. Assume z_0.05= 1.645. A) 0.48± 0.16 B) 0.48± 0.09 C) 0.29± 0.15 D) 0.29± 0.16

Question

Quizplus · Accepted Answer

The sample proportion ($p$) is 12/25 = 0.48. The standard error (SE) for the proportion is calculated using the formula $\sqrt{\frac{p(1-p)}{n}}$, where $n$ is the sample size. Thus, SE = $\sqrt{\frac{0.48(1-0.48)}{25}} = 0.099$. The margin of error (ME) at 90% confidence level, using $z = 1.645$, is ME = $z \times SE = 1.645 \times 0.099 \approx 0.16$. Therefore, the 90% confidence interval is $p \pm ME = 0.48 \pm 0.16$.

In a Sample of 25 IPhones, 12 Had Over 85