Question

a) Decide on appropriate nonparametric statistic for the problem.

b) Show a statistical solution

c) Make a appropriate recommendation based upon your analysis in part b.

Problem 3: Using the data below, determine the best measure of association between price and mileage. Justify your choice of statistic.

Selling Price $	Mileage
29500	61879
19945	86700
28749	55459
28000	105000
21999	41700
30000	33669
38960	16000
23997	65000
28749	55459
30949	29208
24995	100131
39500	23902
20000	83504
34980	34980
33989	49514
29990	48771
20749	108151
33867	19005
31990	35371
12995	101800
18919	116973
28500	37852
24995	64791
24450	15918
42931	7281
13400	145220
40788	19447
50900	7301
22146	47117
23990	78842
29128	48310
19495	80431
27900	51448
13400	145220
12900	167856
24500	67028
22995	101562
26247	73726
11000	139914
38960	16000
24500	98701
23995	58600
28783	78422
47749	34290
18409	79658
31,990	43,639
34,998	32,251
14,458	152,053
30,000	30,669
14,995	128,337
59,786	12,819
23,780	61,561
25,495	122,905
40,890	28,031
17,756	144,386
20,500	95,931
33,889	34,380
29,800	50,409
32,990	32,781
30,901	33,806
15,999	112,250

Answer 1

Problem 3:

Ans: Normality test

Fron the above plot, we know that the Selling price follows a normal distribution but the Mileage does not follow a normal distribution. Hence, we can not use the parametric Pearson correlation test and the suitable test is the nonparametric Spearman rank correlation.

The Spearman rank correlation is

where

ρ= Spearman rank correlation
di= the difference between the ranks of corresponding variables
n= number of observations

The estimated Spearman rank correlation is -0.823 with the p-value of 0.000. Hence, the selling price and mileage have a strong negative relation at 0.05 level of significance.