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 143, 348 runs and had 20 accidents, while the fleet of yellow firetrucks made 135,035 runs and had 4 accidents. At a = .01, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypothesis. (b) Make a 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.
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, = 135,050 runs