Question

# In the study of New York firefighters, the following were the results. No risk for alcohol...

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 793 309 1,102 441 110 551 1,234 419 1,653

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

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.

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