Answer to Question #194729 in Statistics and Probability for Alice

Question

Who knows the game sipa? A physical education major seeks to determine whether all Filipinos are familiar with this game. Among 1,500 respondents, 358 know the game. Use 95% confidence to estimate the population proportion p and q. Interpret the sample data.

Answer 1

$n=1500,p=\dfrac{358}{1500}=0.2387=23.87\%,\ q=76.13\%$

$\alpha=0.05,Z_{\frac{\alpha}{2}}=z_{0.025}=1.96$

population parameter-

$\hat{p}=p\pm Z_{0.025}\sqrt{\dfrac{pq}{n}}$

$=0.2387\pm 1.96 \sqrt{\dfrac{0.2387\times 0.7613}{1500}}\\[9pt]=0.2387\pm 0.02157\\[9pt]=(0.217,0.25027)$