Question 131285
In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate?
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I'd like to compare some of my findings to parts of the question and see how to answer those I was unable to configure.

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I believe this problem has already been answered on the algebra.com site,
but here it is again.
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(a) State the hypotheses.
Ho: p(red)-p(yellow)>0
Ha: p(red)-p(yellow) is not greater than 0
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(b) State the decision rule and sketch it. 
One-tail test with alpha=1%: critical value is z = 2.326
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(c) Find the sample proportions and z test statistic.
p-hat(red)= 20/153,348 ; p-hat(yellow) = 4/135,035
For Pooling: p-barbar = (20+4)/(153348+135035) = 0.00002.08..
z = [(20/153,348)-(4/135,035)]/sqrt[(0.00002.08)(0.999979)/153348 + (0.00002.08)*0.999979/135035)] = 2.960988...
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(d) Make a decision.
Since the test statistic is greater than the critical value, Reject Ho
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(e) Find the p-value and interpret it.
p-value = P(2.960988 < z < 10) = 0.00153...
There is 0.1533% chance that the test would produce stronger evidence 
against Ho.
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(f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
Yes it is statistically significant; the yellow paint has helped reduce 
accidents.
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(g) Is the normality assumption fulfilled? Explain.
Yes: p1n1 > 5 , q1n1>5 ;p2n2 > 5 , p2n2 > 5

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Cheers,
Stan H.