Respuesta :
Answer:
95% confidence interval for the proportion of preschool children vaccinated in that suburb lie between (.5042 , .6958) 0r 50.42% to 69.58%
Step-by-step explanation:
Given -
A random sample of 100 preschool children in Camperdown revealed that only 60 had been vaccinated
Sample size ( n) = 100
Sample proportion [tex](\widehat{p})[/tex] = [tex]\frac{60}{100}[/tex] = 0.6
confidence interval = 95%
[tex]\alpha =[/tex] 1 -.95 = .05
[tex]z_{\frac{\alpha}{2}}[/tex] = [tex]z_{\frac{.05}{2}}[/tex] = 1.96
95% confidence interval for the proportion of preschool children vaccinated in that suburb = [tex]\widehat{p}\pm z_{\frac{\alpha}{2}}\sqrt{\frac{\widehat{p} (1 - \widehat{p})}{n}}[/tex]
= [tex]0.6\pm z_{\frac{.05}{2}}\sqrt{\frac{.6 (1 - .6}{100}}[/tex]
= [tex]0.6\pm 1.96\times.0489[/tex]
= [tex]0.6\pm .0958[/tex]
= (0.6 - .0958) , (0.6 + .0958)
= (.5042 , .6958)
