Question

1) In 2003 the Journal of the American Medical Association reported a study examining the possible impact of air pollution caused by the 9/11 attack on New York's World Trade Center on the weight of babies. Researchers found that 8% of 182 babies born to mothers who were exposed to heavy doses of soot and ash on September 11 were classified as having low birth weight. Only 4% of 2300 babies born in another New York City hospital whose mothers had not been near the site of the disaster were similarly classified. Does this indicate a possibility that air pollution might be linked to a significantly higher proportion of low-weight babies?

a) Perform a Hypothesus Test on the two proportions ( 4 steps). Signuficance level ( 0.05)

Answer 1

Answer:

Given,

Ho : p1 - p2 = 0

Ha : p1 - p2 > 0

sample proportion p1 = x1/n1 = 0.08

p2 = x2/n2 = 0.04

p^ = (x1+x2)/(n1+n2) = 0.043

we know,

p^ + q^ = 1

q^ = 1 - p^

= 1 - 0.043

= 0.957

Here at 0.05 significance level , z value is 1.645

Reject Ho, if z > 1.645

consider,

test statistic z = (p1 - p2)/sqrt(p^q^(1/n1 + 1/n2))

substitute values

= (0.08 - 0.04)/sqrt(0.043*0.957*(1/182 + 1/2300))

= 2.563

P value = P(z > 2.563)

= 0.0051886 [since from z table]

= 0.0052

Here we observe that, p value < alpha, so we reject Ho.

So there is sufficient evidence to support the claim.