Using Nonparametric And Anova Solutions

10.30:Ð' In Dallas, some fire trucks were painted yellow (instead of red) to heighten their visibility. Duringa test period, the fleet of red fire trucks made 153,348 runs and had 20 accidents, while the fleet ofyellow fire trucks made 135,035 runs and had 4 accidents. At О± = .01, did the yellow fire truckshave a significantly lower accident rate? (a) State the hypotheses. (b) State the decision rule andsketch it. (c) Find the sample proportions and z test statistic. (d) Make a decision. (e) Find thep-value and interpret it. (f ) If statistically significant, do you think the difference is large enough tobe important? If so, to whom, and why? (g) Is the normality assumption fulfilled? Explain.Source: The Wall Street Journal, June 26, 1995, p. B1.Accident Rate for Dallas Fire TrucksStatistic Red Fire Trucks Yellow Fire TrucksNumber of accidents x1 = 20 accidents x2 = 4 accidentsNumber of fire runs n1 = 153,348 runs n2 = 135,035 runsANSWER:a). Did the yellow firetrucks have a lower accident rate than the red?1-tailed Z test: Critical Value=2.326b). c). p-bar---(4+20)/(153348+135035)=Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' Ð' 8.3223x10^-5bar=1-p-barz(1.0078x10^-4)=1.0078x10^-4/sqrt[p-bar)(q-bar)/n1+(p-bar)(q-bar)/n2]d). Since the test statistic is greater than the critical value, the hypothesis is rejected.e). p-value = 0.0015 : only 0.15% of the test results could have provided stronger evidence for rejecting the hypothesisf). Yes the difference is large enough to be different.g). p(red)n1>5, q(red)n1>5 and p(yellow)n2>5, q(yellow)n2>510.44:Ð' Does lovastatin (a cholesterol-lowering drug) reduce the risk of heart attack? In a Texas study,researchers gave lovastatin to 2,325 people and an inactive substitute to 2,081 people (average age58). After 5 years, 57 of the lovastatin group had suffered a heart attack, compared with 97 for theinactive pill. (a) State the appropriate hypotheses. (b) Obtain a test statistic and p-value. Interpret the results at О± = .01. (c) Is normality assured? (d) Is the difference large enough to be important?(e) What else would medical researchers need to know before prescribing this drug widely? (Dataare from Science News 153 [May 30, 1998], p. 343.)ANSWER:a). Ho: p(inactive) - p(active) =0Ð' Ð' Ð' Ð' Ha: p(inactive) вЂ" p(active) > 0Ð' p-hat(inactive) = 97/2081 = 0.0466Ð' p-hat(active) = 57/2325 = 0.0245Ð' p-bar = (97+57)/(2081+2325) = 0.0350Ð' q-bar = 1-p-bar = 0.9650Ð' alpha = 1% critical value = z = 2.326b). z(0.0466-0.0245) = (0.0221)/sqrt[(0.035x0.965/2081)+(0.035x0.965/2325)]Ð' Ð' Ð' Ð' Ð' 3.9849Ð' Ð' Ð' Ð' Ð' p-value вЂ" 0.0000338* Because the p-value is less than alpha, the Hypothesis is rejected there is statistical evidence that the application of medicine reduces the incidence of death.c).Ð' 2081x0.035=72.84 > 5 and 2081x0.965 >5Ð' Ð' Ð' Ð' Ð' 2325x0.035=70.86 > 5 and 2325x0.965 >5d). the p-value gives very strong evidence for the hypothesis.e).Ð' if there are any side effect, and if the diet of the other medicated patients were appropriate.10.46:Ð' To test the hypothesis that students who finish an exam first get better grades, Professor Hardtackkept track of the order in which papers were handed