Question 132908This question is from textbook Applied Statistics in Business and Economics
: 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 hypothesis. (b) State the decision rule and sketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find the p-value and interpret it. (f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.
Accident Rate for Dallas Fire Trucks
Statistic Red Fire Trucks Yellow Fire Trucks
Number of accidents X,= 20 accidents X2 = 4 accidents
Number of fire runs N1= 153,348 runs N2= 135,035 runs
This question is from textbook Applied Statistics in Business and Economics
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility.
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During the test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents,
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while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents.
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At a=.01, did the yellow fire trucks have a significantly lower accident rate?
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a) State the hypothesis
Ho: p-hat(red)-p-hat(yellow <=0
Ha: p-hat(red)-p-hat(yellow) > 0
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b) State the decision rule and sketch it.
Critical value for one-tail z-test with alpha=1% = 2.326
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c) Find the sample proportions and = test statistic
Using a TI Calculator and running a 2-Proportion Z-Test I get:
p-hat(red)= 0.0001304223; p-hat(yellow)=0.00002982195
Pooled p-hat = 0.000032226598
test statistic = 2.960988745
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d) Make a decision
Since test stat is greater than critical value, reject Ho.
There were statistically more accidents with the red than with the yellow vehicles.
e) Find the p-value and interpret it
p-value = 0.0015333...; Only 0.0015333 of test results could have shown
stronger evidence that the red had a higher accident rate than the yellow.
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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, the test gave strong evidence that painting the trucks yellow
reduced the accident rate.
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g) Is the normality assumption fulfilled? Explain.
I'll leave that to you.
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Cheers,
Stan H.
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