10.30 - In Dallas, some fire trucks were painted yellow(instead of red) to heigh

Question

10.30 - In Dallas, some fire trucks were painted yellow(instead of red) to heighten their visibiity. During a testperiod, the fleet of red fire trucks made 153,348 runs and had 20accidents, while the fleet of yellow fire trucks made 135,035 runsand had 4 accidents. At a=.01, did the yello fire trucks havea significantly lower accident rate? a) state the hypothesis.b) state the decison rule and sketchit. c) find hte sampleproportions and z test statistic. d) make a decision. e) Find thep-value and interpret it. f) If statistically significant, do youthink the differenc is large enough to be important? If so, to whomand why? g) Is the normality assumption fulfilled. Explain. Red FireTrucks                   Yellow Fire Trucks x1= 20accidents                  x2= 4 accidents n1= 153,348runs                 n2= 135,035 runs Donald helped me with this question somewhat but all partswhere not answered and I need a complete answer to all parts allthe way up to g. Thanks in advance. 10.30 - In Dallas, some fire trucks were painted yellow(instead of red) to heighten their visibiity. During a testperiod, the fleet of red fire trucks made 153,348 runs and had 20accidents, while the fleet of yellow fire trucks made 135,035 runsand had 4 accidents. At a=.01, did the yello fire trucks havea significantly lower accident rate? a) state the hypothesis.b) state the decison rule and sketchit. c) find hte sampleproportions and z test statistic. d) make a decision. e) Find thep-value and interpret it. f) If statistically significant, do youthink the differenc is large enough to be important? If so, to whomand why? g) Is the normality assumption fulfilled. Explain. Red FireTrucks                   Yellow Fire Trucks x1= 20accidents                  x2= 4 accidents n1= 153,348runs                 n2= 135,035 runs Donald helped me with this question somewhat but all partswhere not answered and I need a complete answer to all parts allthe way up to g. Thanks in advance.

Explanation / Answer

For the normality assumption you need at least 10 success in eachgroup, but you only have 4 in the yellow group. There is a way around this, though. Since the null hypothesis isthat p1 = p2, we can assume the samples come from identicalpopulations and pool them: we have a total of 24 successes out of288,383 samples for an overall proportions of 24/288383 =0.000083 153,348*0.000083 = 12.8 > 10 135,035*0.000083 = 11.2 > 10 so the normality assumption is satisfied and it's OK to do theother stuff you went over with Donald.

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