12(9.) Carbon Monoxide From a random sample of 1201 Americans, it was discovered

Question

12(9.) Carbon Monoxide From a random sample of 1201 Americans, it was discovered that 1139 of them lived in neighborhoods with acceptable levels of carbon monoxide. Source: Environmental Protection Agency.

(a) Obtain a point estimate for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide. Round 4 decimals

(b) Construct a 95% confidence interval for the proportion of Americans who live in neighborhoods with acceptable levels of carbon monoxide.

(c) What sample size would be needed for the estimate to be within 1.5 percentage points with 90% confidence if you use the estimate obtained in part (a)? (Hint: Remember to always round UP)

Explanation / Answer

Solution:

a) Given that x = 1139
n = 1201
p = x/n = 1139/1201 = 0.9484
The population proportion x = p
= 0.9484
b) Confidence interval = p ± Z/2 sqrt[p(1-p)/n]
= 0.9484 ± 1.96* sqrt[0.9484(1-0.9484)/1201]
= 0.9484 ± 0.0125
= (0.9359, 0.9609)
c) Z/2 = Z0.05 = 1.645, E = 1.5
p = 0.9484
Sample size n = p(1-p) [Z/2/E]^2
= 0.9484(1-0.9484)[1.645/0.015]^2
=588.55 593

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