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Z test for proportion for fire trucks data

Please solve using the 5 step procedure for Hypothesis testing.
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.
(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 x1 = 20 accidents x2 = 4 accidents
Number of fire runs n1 = 153,348 runs n2 = 135,035 runs

Solution Summary

Step by step method for testing the hypothesis under 5 step approach for fire trucks from Applied Statistics in Business and Economics by David P Doane and Lori E. Seward, McGraw Hill; 1st Edition (2006)

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