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week 3 E text Scott Ward

# week 3 E text Scott Ward - o Chapter Exercises 10.30 In...

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o Chapter Exercises 10.30 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? p-hat (red) = 20 / 153248 = 1.304 x 10 ^ -4 p-hat (yellow) = 4 / 135035 = 2.9622 x 10 ^ -5 (a) State the hypotheses. H o : p (red) – p (yellow) = 0 H 1 : p (red) – p (yellow) < 0 (b) State the decision rule and sketch it. CV with a = 1% = 2.326 (c) Find the sample proportions and z test statistic. p-hat (red) = .0001 p-hat (yellow) = .00002 test stat = [(20 / 153,348) - (4 / 135,035)] / sqrt [(0.00002 + (0.0001) x 0.999979 / 135035 )] = 2.961 (d) Make a decision. The test of 2.96 is larger than the CV of 2.36 so must reject the H 0 (e) Find the p-value and interpret it. p-value = .0015. This means the red trucks had a higher evidence of having more accidents than the yellow trucks. (f) If statistically significant, do you think the difference is large enough to be important? If so, to whom, and why?

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