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In Dallas, some fire trucks were painted yellow (instead of the red) to heighten their visibility. Throughout 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 four accidents. At α = .01, did the yellow fire trucks have significantly lower accident rate?

a) Describe the hypotheses.

b) Describe the decision rule and sketch it.

c) Find out the sample proportions and z test statistic.

d) Make decision.

e) Find out the p-value and interpret it.

f) If statistically significant, do you think the difference is large enough to be significant? If so, to whom, and why?

g) Is the normality assumption fulfilled? describe.

Accident Rate for Dallas Fire Trucks 
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

 

Statistics and Probability, Statistics

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