Posted by G. on .
In Dallas some fire trucks were painted yellow (not red) to heighten their visability. During a test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet of yellow trucks 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) state the decision rule and sketch it (c) find the 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 normally assumption fulfilled? Explain
Accident rate for Dallas Fire Trucks
Statistic Red Trucks Yellow Trucks
# of Accidentsx1=20accidents x2=4accid
# of fire runsn1=153,348 n2=135,035
Ho: pY = pR (R = red trucks; Y = yellow trucks)
Ha: pY < pR
You can use a binomial proportion 2-sample z-test for this kind of problem.
Here is one formula for this type of test:
z = (pY - pR)/√(pq(1/n1 + 1/n2)
p = (x1 + x2)/(n1 + n2)
q = 1 - p
pY = 4/135035
pR = 20/153348
p = (4 + 20)/(135035 + 153348)
q = 1 - p
Convert to decimals and substitute into the formula. Calculate z. Compare to the cutoff z at .01 for a one-tailed test (Ha shows a specific direction, so the test is one-tailed). Determine the p-value, which is the actual level of the test statistic. Determine whether to reject Ho (the null hypothesis) or fail to reject Ho. If you reject Ho, then you accept Ha and the test is statistically significant.
I hope this will help get you started.