Question 198419This question is from textbook
: I have no clue, so could someone please assist me with this problem. I'd really appreciate it.
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.
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?
(a) State the hypotheses.
Ho: p(yellow)-p(red) = 0
Ha: p(yellow)-p(red) < 0
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(b) State the decision rule and sketch it.
Reject Ho if the test statistic is less than -2.326..
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(c) Find the sample proportions and z test statistic.
phat(yellow) = 4/135035
phat(red) = 20/153348
test statistic: z = -2.961
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(d) Make a decision.
Reject Ho.
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(e) Find the p-value and interpret it.
P(z<-2.961 ) = 0.00153...
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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?
(g) Is the normality assumption fulfilled? Explain.
Comment: I'll leave "f" and "g" to you.
Cheers,
Stan H.
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