In the Dallas, some fire trucks were painted yellow (instead of the red colour) 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 the significantly lower accident rate?
(a) State hypotheses.
(b) State decision rule and sketch it.
(c) Find out the sample proportions and z test statistic.
(d) Make a 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.
Source: The Wall Street Journal, June 26, 1995, p. B1.
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