```Question 192135
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,
p-hat(red) = 20/153,348 = 0.0001304
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while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135,035 = 0.00002962
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Difference of sample proportions: 0.0001006
At &#945; = .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 is z > 2.326
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(c) Find the sample proportions and z test statistic.
Using a TI calculator for a 2-Proportion Z-Test I get
z = 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(z>2.961) = 0.0015..
0.015% of test results could have given 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?
I'll leave that to you.
Looks like yellow wins.
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(g) Is the normality assumption fulfilled? Explain
Independence and x < 10%
I'll leave that to you.
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Cheers,
Stan H.
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