Hypothesis testing for the difference between two proportions.
In Dallas, some fire trucks were painted yellow (in its place of 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 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate?
(a) Situation the hypotheses.
(b) State the decision rule and sketch it.
(c) Find out 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? Give details.
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