Question

In the study of New York firefighters, the following were the results.

	No risk for alcohol problems	Moderate to severe risk for alcohol problems	Totals
Participated in 9/11 rescue	793	309	1,102
Did not participate in 9/11 rescue	441	110	551
Totals	1,234	419	1,653

Are the firefighters who participated in the 9/11 rescue at greeater risk of alcohol problems? Support your answer.

Answer 1

Participated:

n1 = 1102

x1 = 309

p̂1 = x1/n1 = 0.2804

Did not participate:

n2 = 551

x2 = 110

p̂2 = x2/n2 = 0.1996

α = 0.05

Null and Alternative hypothesis:

Ho : p1 = p2

H1 : p1 > p2

Pooled proportion:

p̄ = (x1+x2)/(n1+n2) = (309+110)/(1102+551) = 0.2535

Test statistic:

z = (p̂1 - p̂2)/√ [p̄*(1-p̄)*(1/n1+1/n2)] = (0.2804 - 0.1996)/√[0.2535*0.7465*(1/1102+1/551)] = 3.5583

p-value = 1- NORM.S.DIST(3.5583, 1) = 0.0002

Decision:

p-value < α, Reject the null hypothesis

Conclusion:

There is enough evidence to conclude that firefighters who participated in the 9/11 rescue at greater risk of alcohol problems.