Question 417140: 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 _ = .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.
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
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
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p-hat(red) = 20/153,348 = 1.304x10^-4
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yellow fire trucks made 135,035 runs and had 4 accidents.
p-hat(yellow) = 4/135035 = 2.9622x10-5
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At α = .01, did the yellow fire trucks have a significantly lower accident rate?
One-tail z-test: Critical value = 2.326
(a) State the hypothesis.
Ho: p(red)-p(yellow) = 0
Ha: p(red)-p(yellow) < 0
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(b) State the decision rule and sketch it.
? Not sure what is meant by this.
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(c) Find the sample proportions and z test statistic.
Test statistic:
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Note: p-bar= (4+20)/(153348+135035) = 8.3223x10^-5;q-bar=1-p-bar
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Test statistic
z(1.0078x10^-4) = 1.0078x10^-4/sqrt[(p-bar)(q-bar)/n1 + (p-bar)(q-bar)/n2]
= 2.9610
(d) Make a decision.
Since the test statistic is greater than the critical value, reject Ho.
p(red) is not equal to p(yellow)
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(e) Find the p-value and interpret it.
p-value = 0.0015 ; Only 0.15% of test results could have provided stronger
evidence for rejecting 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?
I'll leave that to you
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(g) Is the normality assumption fulfilled? Explain.
Show that p(red)n1>5, q(red)n1>5
and p(yellow)n2>5, q(yellow)n2>5
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Cheers,
Stan H.
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