Two proportions Z test
In Dallas, some fire trucks were painted yellow (instead 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) Declare the hypotheses.
(b) State the decision rule and sketch it.
(c) Find out the sample proportions and z test statistic
(d) Create 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 important? If so to whom and why?
(g) Is the normality assumption fulfilled? Give details.
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