Question

10. + -/4.16 points ASWSBE14 8.E.031. My Notes + Ask Your Teacher You may need to use the appropriate appendix table or technology to answer this question. A simple random sample of 400 individuals provides 148 Yes responses. (a) What is the point estimate of the proportion of the population that would provide Yes responses? (b) What is your estimate of the standard error of the proportion, 0-? (Round your answer to four decimal places.) (c) Compute the 95% confidence interval for the population proportion. (Round your answers to four decimal places.)

Answer 1

a. Point estimate is $p=\frac{148}{400}=0.37$

b. Standard error is $\sigma_p=\sqrt{\frac{pq}{n}}=\sqrt{\frac{0.37*0.63}{400}}=0.0241$

c. z value for 95% CI is 1.96 as P(-1.96<z<1.96)=0.95

So Margin of Error is $E=z*\sigma_p=1.96*0.0241=0.0472$

Hence CI is $CI=p\pm E=0.37\pm 0.0472=(0.3228,0.4172)$