Answer:
The random two-sided 95% confidence interval estimator for p is
(0.5192 , 0.5807)
Step-by-step explanation:
step(i):-
Given toss the coin 1000 times to find 550 of them were heads
given sample size n =1000
x = 550
sample proportion
[tex]p = \frac{x}{n} = \frac{550}{1000} = 0.55[/tex]
[tex]Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96[/tex]
Step(ii):-
The random two-sided 95% confidence interval estimator for p is determined by
[tex](p - Z\frac{\alpha }{2} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z\frac{\alpha }{2} \frac{\sqrt{p(1-p)} }{\sqrt{n} })[/tex]
[tex](0.55 - 1.96 \frac{\sqrt{0.55(1-0.55)} }{\sqrt{1000} } , 0.55 + 1.96 \frac{\sqrt{0.55(1-0.55)} }{\sqrt{1000} })[/tex]
(0.55 - 1.96 X 0.0157 , 0.55 + 1.96 X 0.0157)
(0.5192 , 0.5807)
conclusion:-
The random two-sided 95% confidence interval estimator for p is
(0.5192 , 0.5807)
confidence interval say the Population of proportion is lies between in these interval.
