Question

NAME: 1.24 It is a commonly held belief that SUVs are safer than cars. If an SUV and car are in a collision, does the SUV sustain less damage (as suggested by the cost of repair)? The Insurance Institute for Highway Safety crashed SUVs into cars, with the SUV moving 10 mph and the front of the SUV crashing into the rear or the car. The following data was obtained: (40 PTS) SUV into Car SUV Damage (S) Car Damage (S) Honda CR-V into Honda Civic 1721 1274 Toyota RAV4 into Toyota Corolla 1434 2327 Hyundai Tuscon into Kia Forte 850 Volkswagen Tiguan into VW Golf 2329 Jeep Patriot into Dodge Caliber 1415 3095 Ford Escape into Ford Focus 1470 3386 Nissan Rogue into Nissan Sentra 2884 4560 3223 2058 a) Why is this a matched-pair design? b) Test the claim that the data suggests the cost of repair for the car is higher. Use an a=0.05 level of significance. (When the data was graphed it indicated that the differences are approximately normally distributed with no outliers). i) State the null and alternate hypothesis using correct notation. ii) Compute the mean and standard deviation of the differences (d and Sd). Round to 2 decimal places. d = Sa =

Answer 1

Let d be the difference of costs for repair for SUV and Car. SUV Damage: 1721 1434 850 2329 1415 1470 2884 Car Damage: 1274 2327 3223 2058 3095 3386 4560 Difference de 447 -893 -2373 271 - 1680 -1916 - 1676 a)Since it is the study of amount of damage when two vehicles were met in accident. When accedent is takes place between SUV and Cae then we compare the damage of SUV with that of the corresponding car damage. We should take the data of damagesin pair wise. We should compare the damage of SUV with the car damage whichis met with accedent with same SVU only. Hence we should use paired t-test. We will compute the mean and standard deviation of differences. b) i) H,: 42 = 0 (There is no difference in damages of SUV and car H:Hg <1(ie) SUV's damage costis less. (Left tail test) Level of significance a= 0.05 Degrees of freedom n-1= 7-1= 6 ii) Let d be the mean of differences. 447-893-2373+271 - 1680-1916 -1676 -7820 d = =-1117.143 =-1117.14 7 7 (d, -c)_(447-(-1117.143) +...+(-1916-(-1117.143) + (-1676-(-1117.143) »-1 7-1 = 1211367.143 Jo = 1100.621= 1100.62 d = 1117.14, 0, = 1100.62 d- Test statistic t = where n = 11, is the sample size. - Ha ܕܢ |:6 -1117.143-0 1100.621 -2.6855 77 to at 5% los with 6 degrees of freedom for left tail test is -1.943 (From t-tables) Criterion: If tea <head, We fail to accept Ho Otherwise accept H conclusion : Since tcm =-2.6855 <-1.943 =, H, is Rejected (1.e) H, is accepted. The damage cost of SUV is less than that of cars damage.