Answer to Question #327646 in Statistics and Probability for liza

Question

1. In a learning style study, 1200 respondents were asked if they can assimilate concepts while watching television. 568 said Yes. Find a 95% confidence interval for the population p (Explain your solutions):
2. What is α?
3. What are the confidence coefficients?
4. what are p and q?
5. The error E is approximately?
6. What are the lower and upper limits?
7. The true population proportion falls between?

Answer 1

$1:\alpha =0.05\\2:\\\sqrt{\frac{pq}{n}}z_{1-\frac{\alpha}{2}}\\3:\\p=\frac{568}{1200}=0.473333\\q=1-p=0.526667\\5:\\E=\sqrt{\frac{pq}{n}}z_{1-\frac{\alpha}{2}}=\sqrt{\frac{0.473333\cdot 0.526667}{1200}}\cdot 1.960=0.0282499\\6:\\p-E=0.445083-lower\\p+E=0.501583-upper\\7:\\\left( 0.445083,0.501583 \right)$