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

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