In Dallas, some fire trucks were painted yellow(instead of red) to heighten thei

ID: 2915080 • Letter: I

Question

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 made153,348 runs and had 20 accidents, while the fleetof

yellow fire trucks made 135,035 runs and had 4accidents. At = .01, did the yellow fire trucks

have asignificantly lower accident rate? (a) State the hypotheses. (b)State the decision rule and

sketchit. (c) Find the sample proportions and z test statistic. (d) Make adecision. (e) Find the

p-value and interpret it. (f ) If statisticallysignificant, do you think the difference is large enoughto

beimportant? If so, to whom, and why? (g) Is the normality assumptionfulfilled? Explain.

Source: The Wall Street Journal, June 26, 1995, p. B1.

Accident Rate for Dallas Fire Trucks

Statistic Red Fire Trucks Yellow FireTrucks

Numberof accidents x1 = 20accidents x2 = 4accidents

Numberof fire runs n1 = 153,348 runs n2 = 135,035 runs

b. Reject the null hypothesis if z> 2.326.

c. p1 20/153348 =.0001304, p2 = 4/135035 = .0000296, z = 2.961

d. We reject the null hypothesis. Thesample evidence shows a significant difference in the twoproportions.

e. The p-value = .0031. Thisresult is not due to chance.

f. Yes, accidents have severe consequencestherefore even small reductions make a difference.

g. The normality assumption is questionablebecause there were only 4 accidents observed with the yellow firetrucks.