In Dallas, some fire trucks were painted yellow (instead of red) to heighten the
ID: 2955874 • 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 made 153,348 runs and had 20 accidents, while the fleet of yellow fire 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 hypotheses.
(b) State the 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.
Explanation / Answer
red: n1=153348, p1=20/153348= 0.00013
yellow: n2=135,035, p2=4/135035=0.00002
(a) state the hypotheses
Ho:p1-p1<=0
H1:p1-p2>0
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(b) state the decision rule and sketch it
Given a=0.01, the critical value is |Z(0.01)|=2.33 (check standard normal table)
If Z>2.33, reject Ho.
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(c) find the sample proportions and z test statistic
Z=(p1-p2)/[p1*(1-p1)/n1 + p2*(1-p2)/n2]
=(0.00013-0.00002)/sqrt(0.00013*(1-0.00013)/153348 +0.00002*(1-0.00002)/135035 )
= 3.49
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(d) make a decision
Since Z= 3.49 is larger than 2.33, we reject Ho.
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(e) find the p value and interpret it.
The p-value is P(Z> 3.49)=0.0002 (check standard normal table)
Since p-value is less than a=0.01, we reject Ho.
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(f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?
Yes
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(g) is the normality assumption fulfilled? Explain
Yes