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 49 births at the hospital, 32% were Caesarean sections. Find the 95% confidence interval for the population proportion

Answer: (0.1828,0.4572)Step-by-step explanation:Given : A medical researcher wishes to estimate what proportion of babies born at a particular hospital are born by Caesarean section.Sample size : n= 49Proportion of babies were Caesarean sections : [tex]\hat{p}=0.32[/tex]Significance level : [tex]\alpha =1-0.95=0.05[/tex]Standard error : [tex]S.E.=\sqrt{\dfrac{\hat{p}(1-\hat{p})}{n}}[/tex][tex]=\sqrt{\dfrac{0.32\times0.68}{49}}=0.06663945022\approx0.07[/tex]Margin of error : [tex]E=z_{\alpha/2}\times S.E.[/tex][tex]=z_{0.025}\times0.07=1.96\times0.07=0.1372[/tex]The confidence interval for the population proportion is given by :-[tex]\hat{p}\pm E[/tex][tex]=0.32\pm0.1372=(0.1828,0.4572)[/tex]