Answer:
The correct solution is "(0.092, 0.148)".
Step-by-step explanation:
Given:
Sample size,
n = 500
True proportion,
[tex]\hat {p} = \frac{60}{500}[/tex]
[tex]=0.12[/tex]
The standard error will be:
[tex]SE=\sqrt{\frac{\hat p(1-\hat p)}{n} }[/tex]
[tex]=\sqrt{\frac{0.12(1-0.12)}{500} }[/tex]
[tex]=\frac{0.12(0.88)}{500}[/tex]
The confidence interval is "1.96".
hence,
The required confidence interval will be:
= [tex](\hat p - 1.96 SE, \hat p + 1.96 SE)[/tex]
By substituting the values, we get
= [tex](0.12-1.96\sqrt{\frac{0.12(0.88)}{500} }, 0.12+1.96\sqrt{\frac{0.12(0.88)}{500} } )[/tex]
= [tex](0.092, 0.148)[/tex]
