In Dallas, some fire trucks were painted yellow (instead of red) to heighten the
ID: 2959781 • Letter: I
Question
In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. Duringa test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet ofyellow fire trucks made 135,035 runs and had 4 accidents. At = .01, did the yellow fire truckshave a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule andsketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find thep-value and interpret it. (f ) If statistically significant, do you think the difference is large enough tobe 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 = 135,035 runs
Explanation / Answer
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 153,348 runs and had 20 accidents,
p-hat(red) = 20/153,348 = 0.0001304
---------------------
while the fleet of yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135,035 = 0.00002962
---------------------------------
Difference of sample proportions: 0.0001006
At = .01, did the yellow fire trucks have a significantly lower accident rate?
(a) State the hypotheses.
Ho: p(red) - p(yellow) =0
Ha: p(red) - p(yellow) > 0
--------------------------------
(b) State the decision rule and sketch it.
Reject Ho is z > 2.326
---------------------------
(c) Find the sample proportions and z test statistic.
Using a TI calculator for a 2-Proportion Z-Test I get
z = 2.961
-------------------------------------------------------------------------
(d) Make a decision.
Reject Ho
---------------------------
(e) Find the p-value and interpret it.
P(z>2.961) = 0.0015..
0.015% of test results could have given stronger evidence for rejecting Ho.
------------------------------------
(f ) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
I'll leave that to you.
Looks like yellow wins.
(g) Yes: p1n1 > 5 , q1n1>5 ;p2n2 > 5 , p2n2 > 5