Question 206358
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? 
(a) State the hypotheses. 
Ho: p(red)-p(yellow) = 0
Ha: p(red)-p(yellow) > 0
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(b) State the decision rule and sketch it. 
Reject Ho if the test statistic is greater than z = 2.3263
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(c) Find the sample proportions and z test statistic.
p-hat(red) = 20/153348 ; p-hat(yellow) = 4/135,035 
z-test statistic: 2.961
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(d) Make a decision. 
Reject Ho
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(e) Find the p-value and interpret it. 
p-value: P(z>2.961) = 0.0015
Only 0.15% of test results could provide stronger evidence for
rejecting 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 supports painting all engines yellow
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(g) Is the normality assumption fulfilled? Explain.
The sample sizes are large enough to support the conclusion.
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Cheers,
Stan H.
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Statistic Red Fire Trucks Yellow Fire Trucks
Number of accidents x1 = 20 accidents x2 = 4 accidents
Number of fire runs n1 = 153,348 runs n2 = 135,035 runs