SOLUTION: I just need help setting this question up and the formulas with it thank you A recent survey showed that in a sample of 100 elementary school teachers, 15 smoked. In a sample of

Question 926287: I just need help setting this question up and the formulas with it thank you
A recent survey showed that in a sample of 100 elementary school teachers, 15 smoked. In a sample of 180 high school teachers, 36 smoked. is the proportion of high school teachers who smoke greater than the proportion of elementary schools school teachers who smoke? use alpha=0.01.

Found 2 solutions by rfer, stanbon:
Answer by rfer(16322) (Show Source): You can put this solution on YOUR website!
15/100=0.15=15%
36/180=0.20=20%
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A recent survey showed that in a sample of 100 elementary school teachers, 15 smoked. In a sample of 180 high school teachers, 36 smoked. is the proportion of high school teachers who smoke greater than the proportion of elementary schools school teachers who smoke? use alpha=0.01.
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element p1-hat = 0.15
h.s. p2-hat = 36/80 = 0.2
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Test:: Is hs greater than elem
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Ho: p2 - p1 <= 0
Ha: p2 - pa > 0 (claim)
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Sample proportion:: p2-hat - p1-hat = 0.2-0.15 = 0.05
test stat formula z(p1-p1) = [(p2-hat-p1-hat)-(0]/sqrt[(pq/n1+pq/n2]
test statistic:: z(0.05) = (0.05)/[sqrt{(0.15*0.2/100)+(0.15*0.2/180)] = 2.3146
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p-value = P(z > 2.3146) = 0.0103
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Conclusion:: Since the p-value equals alpha, the test is inconclusive.
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Cheers,
Stan H.
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