Question 131285This question is from textbook
: Hello Tutors,
Please assist me with the following 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 α = .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.
I'd like to compare some of my findings to parts of the question and see how to answer those I was unable to configure.
This question is from textbook
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 yellow fire trucks made 135,035 runs and had 4 accidents. At α = .01, did the yellow fire trucks have a significantly lower accident rate?
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I'd like to compare some of my findings to parts of the question and see how to answer those I was unable to configure.
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I believe this problem has already been answered on the algebra.com site,
but here it is again.
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(a) State the hypotheses.
Ho: p(red)-p(yellow)>0
Ha: p(red)-p(yellow) is not greater than 0
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(b) State the decision rule and sketch it.
One-tail test with alpha=1%: critical value is z = 2.326
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(c) Find the sample proportions and z test statistic.
p-hat(red)= 20/153,348 ; p-hat(yellow) = 4/135,035
For Pooling: p-barbar = (20+4)/(153348+135035) = 0.00002.08..
z = [(20/153,348)-(4/135,035)]/sqrt[(0.00002.08)(0.999979)/153348 + (0.00002.08)*0.999979/135035)] = 2.960988...
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(d) Make a decision.
Since the test statistic is greater than the critical value, Reject Ho
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(e) Find the p-value and interpret it.
p-value = P(2.960988 < z < 10) = 0.00153...
There is 0.1533% chance that the test would produce stronger evidence
against 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 it is statistically significant; the yellow paint has helped reduce
accidents.
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(g) Is the normality assumption fulfilled? Explain.
Yes: p1n1 > 5 , q1n1>5 ;p2n2 > 5 , p2n2 > 5
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Cheers,
Stan H.
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