Question

6. A car manufacturer claims that one of their models, let's call it Mendel A, on average has a significantly shorter stopping distance than a competition's model, let's call it Model B, in the same class. To test their claim the distance (in feet) it took for 8 Model A cars to get to Complete stop from 60 miles per hour was recorder. The same was done for 9 Model B cars. The result were as follows. Model A: 98, 97, 99, 101, 95, 99, 100, 95 Model B: 94, 101, 100, 102, 100, 99, 97, 102, 96 (A) 3 Calculate the ratio of the maximum sample variance to the minimum sample variance. Does it appear that the population variances are equal or (B) At 5% level of significance is there sufficient evidence to indicate that the claim of the unequal? Explain. manufacturer of Model A is true? Use the critical value approach. (C) 12 What is the p-value for the test in (B)? (D) 1] Is it necessary to assume that the populations are normally distributed to validate the test in (B)?

Answer 1

6- _2.9039 2.2039 6). That 781 - 98 Sat Janei, caut (Party = (76866– (zgye) = are you go 76 = 150- Sql = 99 Se vorenting (993-cotets) - SC8827 - (0925) = 2.7839 4. Ho: 2 vs Haid Statistie fase faze 3932 = 15956.. & P-value = 16 equal 778 df = (8,7) , P-value = 0.2759 - P-value x 0.10. So fail to reject to Conclusion: we can conclude that the population variances are B). Pooler ariance Salba-1) så thg-)) Só 742.9039) 48/.783aqj) (14-17+ ingin s'z 6-4001. Claim: on average has a sufficiently shorter stopping distance them Comptation models for a compared to R. (i) Ho: MA= MB Versux Ha: MA< MB. (1) at &-5% (0.05) level of significance df=(0A-1) + (08-1) = 7+8=15 reject to it ta-1-753. (111) The test statistic t=PA5B - (98-99) VS² Chat the 6.4001 ly tha) (1) Decision: fail to reject to E- 0.8135 Conclusion: No sutticent usion: No sutti cent eviden evidence support the claim. to of manutacture A. (6) P-value = 0.2143 (D) yes, the normality assumption for populations are needed and very necessary.