We can also use non parametric test to analyze the sample of car sales collected. I will use Mann-Whitney U test to further investigate if there is a difference between the two population I.e. population of imported cars sold and domestic cars as differentiated by the “type” column.

SAMPLE 1(DOMESTIC CARS)
SAMPLE 2 (IMPORTED CARS)
Price($000)
Age
Type
Rank
Price($000)
Age
Type
Rank
23.197
46
0
43
20.454
40
1
25
23.372
48
0
44
26.651
46
1
65
23.591
40
0
45
27.453
37
1
68
30.872
32
0
76
17.266
32
1
4
19.587
47
0
14
18.021
29
1
9
23.169
56
0
42
28.683
38
1
73
35.851
42
0
79
19.251
42
1
12
24.285
50
0
51
20.047
28
1
20
25.277
38
0
58
24.324
50
1
53
24.533
39
0
54
24.609
31
1
56
27.443
44
0
67
28.67
51
1
72
23.657
42
0
47
15.546
26
1
1
20.895
36
0
30
15.935
25
1
3
23.765
53
0
48
19.873
45
1
17
32.277
39
0
77
25.251
56
1
57
24.052
44
0
49
28.034
38
1
70
25.799
30
0
61
19.889
44
1
18
35.925
29
0
80
20.004
46
1
19
20.356
41
0
23
17.357
28
1
5
21.722
35
0
35
20.155
33
1
21
26.285
37
0
63
19.688
35
1
15
27.896
42
0
69
26.613
42
1
64
32.492
31
0
78
20.203
36
1
22
21.74
53
0
36
25.783
53
1
60
22.374
55
0
38
26.661
46
1
66
25.449
46
0
59
20.642
39
1
27
28.337
35
0
71
21.981
43
1
37
30.655
41
0
75
15.794
30
1
2
26.237
34
0
62
18.263
39
1
10
24.296
47
0
52
17.399
29
1
6
Sum of rank (R1)
1626
17.968
30
1
8
No. of observations (n1)
30
21.442
41
1
32

19.331
35
1
13

22.817
51
1
40

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19.766
44
1
16

20.633
51
1
26

20.962
49
1
31

22.845
41
1
41

29.076
42
1
74

18.89
31
1
11

24.571
55
1
55

20.642
35
1
27

23.613
47
1
46

24.22
58
1
50

22.442
41
1
39

17.891
33
1
7

20.818
46
1
29

20.445
34
1
24

21.556
43
1
33

21.639
37
1
34

Sum of rank (R2)
1613

No. of observations (n2)
50

Hypothesis

We found out that international cars are significantly more than domestic cars thus we want to find out if there is a difference in prices of imported cars and domestic cars.

Null Hypothesis: There is no difference between the price of imported automobile and                                domestic automobile

Alternate Hypothesis: Domestic cars are more expensive than imported cars.

I.e.   Ho : U1  = U2

        H1 : U1  > U2

Left- tailed test

?  = 0.05

In formulating the Mann-Whitney U test

U1 = R1 – n1 (n1 + 1) = 1626 – 30(30+1) = 1161

                              2                                  2

U2 = R2 – n2 (n2 + 1) = 1613 – 50(50 +1) =  338

2                                  2

                                          Where R1 is the sum of rank in sample 1

                                                                                R2  is the sum of rank in sample 2

                                                                                n1 is the no. of observations in sample 1

                                                                                n2 is the no. of observations in sample 2

Since the sample is large enough I.e. above 20 then we can use normal approximation, for the z – test we choose the minimum of U1 and U2  for testing I.e. Z test to estimate Mann-Whitney U test such that:

Given      µ = n1n2      and ? = ? n1n2(n1 + n2 + 1)  then   Z = U – µ

                                   2                                   12                                  ?

? = ? 30(50)(30 +50 + 1)  = 100.6231                  µ = 30*50/2 = 750

         12

***Calculated Z = (338 – 750)/100.6231 = – 4.095

*** Critical Z = (left – tailed) =  – Z0.05 = -1.645

*** Calculated Z < critical Z I.e.  -4.095<-1.645. Therefore reject null hypothesis.

Conclusion.

At 95% level of confidence we are sure that domestic automobile are more expensive than international automobile, the test provided sufficient evidence that supported the alternate hypothesis over the null.

            This experiment complements week 3’s experiment in the sense that while in week 3 I looked at the proportion of domestic car buyers and domestic car buyers, I have now tested if there is a significant difference between international prices and domestic prices of cars. The results obtained  are in tandem with the earlier test (Week 3 results) which showed that the number of international automobile buyers are significantly larger than domestic car buyers and this can be explained by the fact that we have shown that domestic prices are significantly higher than international car prices.

Mann-Whitney U test

Mann-Whitney U test is a non parametric test that I used to test whether two samples are drawn from the same population by testing if they have the same median. It is one of the most effective non parametric tests that is used as an alternative to students T-test. Mann Whitney was suitable for this experiment because:

·                                             It tests whether the samples were drawn from the same population and can further

            be used to determine whether observation in one sample tend to be lager than the           other. (Shier, 2004).

·                                             It is easy to calculate since it is possible to approximate U test using Z test (Shier, 2004).

REFERENCE:

Shier, R. (2004). Statistics 2.3: Mann- Whitney U test. Accessed 4th August 2008 from             http://mlsc.lboro.ac.uk/resources/statistics/Mannwhitney.pdf

 

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