A simple random sample was conducted to select 1600 of 100,000 subscribers to an educational research journal.The selected participants were asked whether the journal should increase its base of research coverage to include more social science articles.40% of participants requested an expansion in coverage.What is the 99% confidence interval for the proportion of subscribers who would like a wider research coverage?
A)[.30,.50]
B)[.32,.48]
C)[.33,.44]
D)[.37,.43]

Question

Quizplus · Accepted Answer

The 99% confidence interval for a proportion is 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, and $n$ is the sample size. For a 99% confidence level, the z-score is approximately 2.576. Given $p = 0.40$ and $n = 1600$, the calculation is $0.40 \pm 2.576\sqrt{\frac{0.40(0.60)}{1600}}$, which results in an interval of approximately $[0.37, 0.43]$.

A Simple Random Sample Was Conducted to Select 1600 of 100,000