Question

18. A random sample of 100 preschool children in Camperdown revealed that only 60 had been vaccinated. Provide an approximate 95% confidence interval for the proportion of preschool children vaccinated in that suburb.

Answer 1

95% confidence interval for the proportion of preschool children vaccinated in that suburb lie between (.5042 , .6958) 0r 50.42% to 69.58%

Explanation:

Given -

A random sample of 100 preschool children in Camperdown revealed that only 60 had been vaccinated

Sample size ( n) = 100

Sample proportion
`(\widehat{p})` =
`(60)/(100)` = 0.6

confidence interval = 95%

`\alpha =` 1 -.95 = .05

`z_{(\alpha)/(2)}` =
`z_{(.05)/(2)}` = 1.96

95% confidence interval for the proportion of preschool children vaccinated in that suburb =
`\widehat{p}\pm z_{(\alpha)/(2)}\sqrt{\frac{\widehat{p} (1 - \widehat{p})}{n}}`

=
`0.6\pm z_{(.05)/(2)}\sqrt{(.6 (1 - .6)/(100)}`

=
`0.6\pm 1.96*.0489`

=
`0.6\pm .0958`

= (0.6 - .0958) , (0.6 + .0958)

= (.5042 , .6958)