SOLUTION: Kindly help me in answering as well as understanding the following statistical problem.
In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibili
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Question 126159This question is from textbook Applied Statistics in Business and Economics
: Kindly help me in answering as well as understanding the following statistical problem.
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 the .01 level of significance, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypothesis. (b) State the decision rule. (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 Applied Statistics in Business and Economics
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
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 the .01 level of significance, did the yellow fire trucks have a significantly lower accident rate? (a) State the hypothesis. (b) State the decision rule. (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.
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Ho: p(red)-p(yellow) < 0
Ha: p(red)-p(yellow) >=0
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alpha = 1% ; critical value is z=-2.326348...
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Test Statistic: z[(20/153,348)-(4/135,035)] /(standard deviation) = 2.960989
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p-value = 0.001533
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Conclusion: Reject Ho because p-value is less than 1%
The yellow proportion was significantly lower as shown by the low p-value (or test statistic whihc is less than the critical value).
g) n1p1 is not greater than 5 and n2p2 is not greater than 5 so
normality assumption is not fulfilled
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Cheers,
Stan H.
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