Of 1000 randomly selected cases of lung cancer 844 resulted

Of 1000 randomly selected cases of lung cancer, 844 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. Use a z-score rounded to 2 decimal places.

Round your answers to 3 decimal places.

Of 1000 randomly selected cases of lung cancer, 844 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. Use a z-score rounded to 2 decimal places. Round your answers to 3 decimal places. (a) Using the point estimate of P ? P is less than 0.03, regardless of the true value of P is less than 0.03? (b) How large must the sample if we wish to be at least 95% confident that the error in estimating P obtained from the preliminary sample, what sample size is needed to be 95% confident that the error in estimating the true value of

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

p=844/1000 = 0.844

So the lower bound is

p - Z*sqrt(p*(1-p)/n) = 0.844- 1.96*sqrt(0.844*(1-0.844)/1000) =0.82

So the upper bound is

p + Z*sqrt(p*(1-p)/n) = 0.844+ 1.96*sqrt(0.844*(1-0.844)/1000) =0.87

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(a)

n=(Z/E)^2*p*(1-p)

=(1.96/0.03)^2*0.844*(1-0.844)

=562.0005

Take n=563

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(b) We use p=0.5 as estimated.

n=(Z/E)^2*p*(1-p)

=(1.96/0.03)^2*0.5*(1-0.5)

=1067.111

Take n=1068