Question

Many people purchase SUV because they think they are sturdier and hence safer than regular cars. However data have indicated that the costs of repair of SUV are higher that midsize cars when both cars are in an accident. A random sample of 8 new SUV and midsize cars is tested for front impact resistance. The amount of damage in hundreds of dollars to the vehicles when crashed at 20mph are recorded below. Questions: 1. Is this an independent data or paired? 2. which non-parametric test will be appropriate. rank the data using table 3. test to determine if there is a difference in the distribution of cost of repairs for the cars. use nonparametric test.- critical region=0.05 car 1 2 3 4 5 6 7 8 SUv 14.23 12.47 14.00 13.17 27.48 12.42 32.58 12.98 midsize 11.97 11.42 13. 27 9.87 10.12 10.36 12.65 25.23

Answer 1

1) this is an independent data as there is no matched pair data.

2) for independent data , mann whitney u test will be appropriate

sample 1	sample 2	rank for sample 1	rank for sample 2
14.23	11.97	13	5
12.47	11.42	7	4
14	13.27	12	11
13.17	9.87	10	1
27.48	10.12	15	2
12.42	10.36	6	3
32.58	12.65	16	8
12.98	25.23	9	14

3)

Ho:there is no difference in the distribution of cost of repairs for the cars

H1:there is a difference in the distribution of cost of repairs for the cars

Level of Significance , α =    0.05
  
sample 1  
sample size ,n1 =    8
sum of ranks, R1 =    88
  
U1 = n1*n2+0.5*n1*(n1+1) - R1 =    12
  
sample 2  
sample size ,n2 =    8
sum of ranks , R2=   48
  
U2 = n1*n2 + 0.5*n2*(n2+1) - R2 =   52
  
U-stat= smaller of U1 and U2 =    12
critical value of U=13

since,U-stat<U-critical , reject the null hypothesis

so, there is enough evidence that there is a difference in the distribution of cost of repairs for the cars