From a random sample of 1000 Americans, it was discovered that 920 of them lived

Question

From a random sample of 1000 Americans, it was discovered that 920 of them lived in neighborhoods with acceptable levels of Carbon Monoxide. (Source: The Environmental Protection Agency) Obtain a point estimate for the proportion of Americas who live in neighborhoods with acceptable levels of carbon monoxide. · Construct a 90% confidence interval for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. · Construct a 99% confidence interval for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. ·

Explanation / Answer

a) p is 920/1000=0.92

b) z for 90% confidence is 1.65 thus the lower bound is p-z*sqrt(p*(1-p)/N)=0.92-1.65*sqrt(0.92*(1-0.92)/1000)=0.9058 and the upper bound is p+z*sqrt(p*(1-p)/N)=0.92+1.65*sqrt(0.92*(1-0.92)/1000)=0.9342

c) z for 99% confidence is 2.576 thus lower bound is p-z*sqrt(p*(1-p)/N)=0.92-2.576*sqrt(0.92*(1-0.92)/1000)=0.8979 and the upper bound is p+z*sqrt(p*(1-p)/N)=0.92+2.576*sqrt(0.92*(1-0.92)/1000)=0.9421

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