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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 153348 runs and had 20 accidents while the flee?
Wiki User
∙ 13y ago
a) State the hypotheses.
Ho: p (red)-p (yellow) <=0
Ha: p (red)-p (yellow) >0
(b) State the decision rule and sketch it.
One-tail test with alpha=1%: critical value is z = 2.326
(c) Find the sample proportions and z test statistic.
p-hat(red)= 20/153,348 ; p-hat(yellow) = 4/135,035
For Pooling: p-bar = (20+4)/(153348+135035) = 0.00002.08..
z = [(20/153,348)-(4/135,035)]/√(0.00002... + (0.00002.08)*0.999979/135035)]
= 2.961.
(d) Make a decision.
Test statistic is greater than the critical value. I Reject Ho
(e) Find the p-value and interpret it.
p-value = P(2.960988 < z < 10) = 0.00153
This means that there is a 0.1533% chance that the test would produce stronger evidence that the read had a higher accident rate than yellow.
(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 evidence indicates that yellow paint has helped reduce the number of accidents.
(g) Is the normality assumption fulfilled? Explain.
Yes, p1n1 > 5 , q1n1>5 ;p2n2 > 5 , p2n2 > 5
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∙ 13y ago
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