Of 1000 randomly selected cases of lung cancer 843 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer. a) Construct a 95% two-sides confidence interval on the death rate from lung cancer. Round your answer 3 decimal places. ?≤p≤? b) Using the point estimate of p obtained from the preliminary sample what sample size is needed to be 95% confident that the error in estimatimating the true value of p is less than 0.00? c) How large must the sample if we wish to be at least 95% confident that the error in estimating p is less than 0.03 regardless of the value of p?

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Of 1000 randomly selected cases of lung cancer 843 resulted in death within 10 years. Construct a 95% two-sided confidence interval on the death rate from lung cancer.  a) Construct a 95% two-sides confidence interval on the death rate from lung cancer. Round your answer 3 decimal places.  ?≤p≤?  b) Using the point estimate of p obtained from the preliminary sample what sample size is needed to be 95% confident that the error in estimatimating the true value of p is less than 0.00?  c) How large must the sample if we wish to be at least 95% confident that the error in estimating p is less than 0.03 regardless of the value of p?

facas9 · Accepted Answer

a. Consider the&amp;nbsp;n=1000&amp;nbsp;and&amp;nbsp;x=843. The point estimate is,&amp;nbsp;P^=1−0.843=0.157At&amp;nbsp;95%&amp;nbsp;confidence level.α=1−0.95α=0.05α2=0.025Zα2=Z0.025Zα2=1.960The margin of the error is,E=Zα2p^(1−p^)n=1.960.843(0.157)1000=0.023So, the&amp;nbsp;95%&amp;nbsp;confidence interval for the population p0.843−0.023≤p≤0.843+0.0230.820≤p≤0.866b. Consider the margin error,E=0.03n=(Zα2E)2P^(1−P^)=(1.960.03)20.843×0.157=564.93=565c. &amp;nbsp;For p less than 0.03, the sample size is obtained as,n=(Zα2E)2P^(1−P^)=(1.960.03)20.5×0.5=1067.11=1068

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