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. formally test to determine if there is a difference in the distribution of cost of repairs for the cars use nonparametric test critical rejection region and alpha =0.5

4.what is the p-value compared to the test statistics

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

Please provide details. thank you

Answer 1

(1) This is independent data

(2) Mann-Whitney test

(3) Ho: μ(SUV) = μ(Midsize) and Ha: μ(SUV) ≠ μ(Midsize)

Wilcoxon - Mann/Whitney Test
	n	sum of ranks
	8	89	SUV
	8	47	Midsize
	16	136	total
		68.000	expected value
		9.522	standard deviation
		2.205	z
		.0274	p-value (two-tailed)
No.	Label	Data	Rank
1	SUV	14023	16
2	SUV	12.47	7
3	SUV	14	12
4	SUV	13.17	10
5	SUV	27.48	14
6	SUV	12.42	6
7	SUV	32.58	15
8	SUV	12.98	9
9	Midsize	11.97	5
10	Midsize	11.42	4
11	Midsize	13.27	11
12	Midsize	9.87	1
13	Midsize	10.12	2
14	Midsize	10.36	3
15	Midsize	12.65	8
16	Midsize	25.23	13

(4) p- value = 0.0274

Since this is < 0.05, we reject Ho and accept Ha, and conclude that there is a significant difference between the repair costs of SUVs and Midsize cars.