Question

g Suppose we toss the coin 1000 times to find 550 of them were heads. Use large sample approximation to find the random two-sided 95% confidence interval estimator for p. What does the confidence interval say about true probability of heads for the coin

Answer 1

The random two-sided 95% confidence interval estimator for p is

(0.5192 , 0.5807)

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

`p = (x)/(n) = (550)/(1000) = 0.55`

`Z_{(0.05)/(2) } = Z_(0.025) = 1.96`

Step(ii):-

The random two-sided 95% confidence interval estimator for p is determined by

`(p - Z(\alpha )/(2) (√(p(1-p)) )/(√(n) ) , p + Z(\alpha )/(2) (√(p(1-p)) )/(√(n) ))`

`(0.55 - 1.96 (√(0.55(1-0.55)) )/(√(1000) ) , 0.55 + 1.96 (√(0.55(1-0.55)) )/(√(1000) ))`

(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.