Mathematics: 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

I believe it would be 5/1 because it rise over run...

g Suppose we toss the coin 1000 times to find 550 - id10005506854452, Bellzers8328

jose9794

29.01.2022

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

$p = \frac{x}{n} = \frac{550}{1000} = 0.55$

$Z_{\frac{0.05}{2} } = Z_{0.025} = 1.96$

Step(ii):-

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

$(p - Z\frac{\alpha }{2} \frac{\sqrt{p(1-p)} }{\sqrt{n} } , p + Z\frac{\alpha }{2} \frac{\sqrt{p(1-p)} }{\sqrt{n} })$

$(0.55 - 1.96 \frac{\sqrt{0.55(1-0.55)} }{\sqrt{1000} } , 0.55 + 1.96 \frac{\sqrt{0.55(1-0.55)} }{\sqrt{1000} })$

(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.

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