A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by Caesarean section. In a random sample of 144 births at the hospital, 29\% were Caesarean sections. Find the $95 \%$ confidence interval for the population proportion.
A) $0.2067

Question

A population proportion is to be estimated from the sample described. Approximate the 95% confidence interval. Round your answer to four decimal places, if necessary.
-A medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by Caesarean section. In a random sample of 144 births at the hospital, 29\% were Caesarean sections. Find the $95 \%$ confidence interval for the population proportion.
A) $0.2067 < \mathrm { p } < 0.3733$
B) $0.2365 < \mathrm { p } < 0.3435$
C) $0.2837 < \mathrm { p } < 0.2963$
D) $0.2144 < \mathrm { p } < 0.3656$

Quizplus · Accepted Answer

The sample proportion is 0.29. The standard error is calculated as $\sqrt{(0.29 \times 0.71) / 144}$. The 95% confidence interval is then $0.29 \pm 1.96 \times \text{standard error}$, which gives the interval $0.2144 < p < 0.3656$.

A Population Proportion Is to Be Estimated from the Sample 95%95 \%95%

A Population Proportion Is to Be Estimated from the Sample $95 \%$