Question

The rollover rate of sport utility vehicles is a transportation safety issue. Safety advocates claim that manufacturer A's vehicle has a higher rollover rate than that of manufacturer B. One hundred crashes for each of these vehicles were examined. The rollover rates were pa = 0.35 and PB = 0.25. (a) Does manufacturer A's vehicle have a higher population rollover rate than manufacturer B? Use a=0.10. (b) Compute the appropriate 90% confidence interval corresponding to your test in part (a).

Answer 1

solution: Given - - PA = 0.35 PB = 0. 25 n=10o, n =100 X = PAX n. = 0.35% 100 X = 35 X, = a ×n, = 0.25 X 100 Yg = 25 35+25 loot100 - 0.3 n, the Hypothesis Test statistic I Ho: PA = PB H, PAJPB PA-PB Viltop) ( (Right tailed test) 0.35-0.25 70-34-03) (too toto 1.54 z = By using Poralue approach p.value at Z=1054 is - P-value (0.0619) i Null Hypothesis is 0.0614 (0.10) Rejected. -value

- Conchesion There is enough evidence for manufacturer A's rechicle have a higher Population rollover rate than manufacturer B. 6 At go% (@=01) 1.645. (PA-PB + 2a PA (PA) + PB (1-PB) 8-35-0.25 + 1.645 0.25 (1-0-25) 10.35(1-035) Too CI = (-0.006, 0- 206)