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Week 3 E-Text assignment

Week 3 E-Text assignment - Week 3 E-Text Assignment 10.30...

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Week 3 E-Text Assignment 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? (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. a) 0 : 0 : 2 1 2 1 0 - = - p p H p p H A p1 = red trucks, p2 = yellow trucks b) Reject the null hypothesis if z > 2.3263 2.3263 > shaded area c) 961 . 2 035 , 135 1 348 , 153 1 ) 10 322 . 8 1 ( 10 322 . 8 035 , 135 4 348 , 153 20 1 1 ) 1 ( 10 322 . 8 035 , 135 348 , 153 4 20 5 5 2 1 2 1 5 2 1 2 1 = + - - = + - - = × = + + = + + = - - - x x n n p p p p z n n x x p excel stats = Hypothesis test for two independent proportions p1 p2 p c 0.00013 2.96E-05 8.32E-05 p (as decimal) 0.00013 2.96E-05 8.32E-05 p (as fraction) 20 4 24 X 153348 135035 288383

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