In a sample of 23 iPhones, 10 had over 83 apps downloaded. Construct a 90% confidence interval for the population proportion of all iPhones that obtain over 83 apps. Assume z_0.05= 1.645. A) 0.43± 0.17 B) 0.43± 0.08 C) 0.27± 0.16 D) 0.27± 0.17

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Quizplus · Accepted Answer

The sample proportion ($p$) is 10/23. The margin of error (E) is calculated using the formula $E = z \sqrt{\frac{p(1-p)}{n}}$, where $z$ is the z-score for the confidence level (1.645 for 90%), $p$ is the sample proportion, and $n$ is the sample size. Plugging in the values, $E = 1.645 \sqrt{\frac{(10/23)(1-10/23)}{23}} \approx 0.17$. The confidence interval is then $p \pm E = 0.43 \pm 0.17$.

In a Sample of 23 IPhones, 10 Had Over 83