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Many people purchase SUV because they think they are sturdier and hence safer than regular cars....

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Statistics

Many people purchase SUV because they think they are sturdierand hence safer than regular cars. However data have indicated thatthe costs of repair of SUV are higher that midsize cars when bothcars are in an accident. A random sample of 8 new SUV and midsizecars is tested for front impact resistance. The amount of damage inhundreds of dollars to the vehicles when crashed at 20mph arerecorded below.

Questions: 1. Is this an independent data or paired?

2. Which non-parametric test will be appropriate. Rank the datausing table

3. formally test to determine if there is a difference in thedistribution of cost of repairs for the cars use nonparametric testcritical 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   9.8710.12   10.36   12.65   25.23

Please provide details. thank you

Answer & Explanation Solved by verified expert
4.4 Ratings (772 Votes)

(1) This is independent data

(2) Mann-Whitney test

(3) Ho: ?(SUV) = ?(Midsize) and Ha: ?(SUV) ? ?(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.
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