Question

Rates of return on 24 mutual funds are shown.

Fund	12-Mo.			5-Year
1		7.9			4.0
2		2.9			3.4
3		14.2			7.9
4		5.5			9.8
5		5.1			6.9
6		10.2			12.1
7		3.7			7.8
8		7.8			11.4
9		10.4			15.1
10		12.6			5.5
11		10.0			9.4
12		13.4			2.7
13		-0.7			12.2
14		5.3			4.8
15		21.1			13.2
16		11.7			4.7
17		-1.8			6.4
18		-2.7			-2.7
19		13.7			8.3
20		11.2			8.5
21		8.9			5.0
22		0.9			6.2
23		1.2			12.5
24		11.3			10.4

(a) Fill in the right side of the worksheet below. (Rank values lowest to highest by giving the lowest value a rank =1.)
  

Fund	Rank 12-Mo.		Rank 5-Year
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
Total

(b) Calculate Spearman's rank correlation coefficient. (Round your answer to 3 decimal places. Use the book's formula to determine the coefficient. If you use MegaStat to check answers, you must use version 10.2 Release 2.1 or higher. Ensure the box marked “correct for ties” is NOT checked. Connect's answers follow the textbook method, which does not correct for ties.)
  
Rank correlation coefficient            

(c) Can the assumption of zero correlation be rejected?
  

• No

• Yes

(d) Calculate the Pearson correlation coefficient. (Round your answer to 4 decimal places.)
  
Pearson correlation coefficient            

(e) Could either test be used for this data?
  

• Yes, the data are ratio data.

• No, the data are nominal data.

Answer 1

(a)

Fund 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Rank 12-Mo 12.00 6.00 23.00 10.00 8.00 15.00 7.00 11.00 16.00 20.00 14.00 21.00 3.00 9.00 24.00 19.00 2.00 1.00 22.00 17.00 13.00 4.00 5.00 18.00

Rank 5-Year 4.00 3.00 13.00 17.00 11.00 20.00 12.00 19.00 24.00 8.00 16.00 2.00 21.00 6.00 23.00 5.00 10.00 1.00 14.00 15.00 7.00 9.00 22.00 18.00

(d)

spearsman rank correlation coefficient:

r_s=

di= difference between ranks.

Rank 12-Mo	Rank 5-Year	di	di^2
12	4	8	64
6	3	3	9
23	13	10	100
10	17	-7	49
8	11	-3	9
15	20	-5	25
7	12	-5	25
11	19	-8	64
16	24	-8	64
20	8	12	144
14	16	-2	4
21	2	19	361
3	21	-18	324
9	6	3	9
24	23	1	1
19	5	14	196
2	10	-8	64
1	1	0	0
22	14	8	64
17	15	2	4
13	7	6	36
4	9	-5	25
5	22	-17	289
18	18	0	0

=1930

r_s==0.1608 (calculated)

(b)r_s at 0.05 for 24 samples =0.388 (tabulated)

since r_{s cal}<r_{s tab}  

_{hence, no rejection.}

(c)Pearson correlation coefficient=

X Values 7.9 2.9 14.2 5.5 5.1 10.2 3.7 7.8 10.4 12.6 10.0 13.4 -0.7 5.3 21.1 11.7 -1.8 -2.7 13.7 11.2 8.9 0.9 1.2 11.3

Y Values 4 3.4 7.9 9.8 6.9 12.1 7.8 11.4 15.1 5.5 9.4 2.7 12.2 4.8 13.2 4.7 6.4 -2.7 8.3 8.5 5 6.2 12.5 10.4

X - 0.242 -4.758 6.542 -2.158 -2.558 2.542 -3.958 0.142 2.742 4.942 2.342 5.742 -8.358 -2.358 13.442 4.042 -9.458 -10.358 6.042 3.542 1.242 -6.758 -6.458 3.642

Y - -3.729 -4.329 0.171 2.071 -0.829 4.371 0.071 3.671 7.371 -2.229 1.671 -5.029 4.471 -2.929 5.471 -3.029 -1.329 -10.429 0.571 0.771 -2.729 -1.529 4.771 2.671

(X - )2 0.058 22.642 42.793 4.658 6.545 6.460 15.668 0.020 7.517 24.420 5.483 32.967 69.862 5.562 180.678 16.335 89.460 107.295 36.502 12.543 1.542 45.675 41.710 13.262

(Y - )2 13.907 18.742 0.029 4.288 0.688 19.104 0.005 13.475 54.329 4.969 2.792 25.293 19.988 8.580 29.930 9.176 1.767 108.768 0.326 0.594 7.448 2.338 22.761 7.133

(X - )(Y - ) -0.901 20.600 1.118 -4.470 2.121 11.109 -0.280 0.520 20.208 -11.016 3.913 -28.876 -37.369 6.908 73.537 -12.243 12.572 108.029 3.449 2.730 -3.389 10.335 -30.812 9.726

Key X: X Values Y: Y Values : Mean of X Values : Mean of Y Values X - & Y - : Deviation scores (X - )2 & (Y - )2: Deviation Squared (X - )(Y - ): Product of Deviation Scores

Result Details & Calculation X Values ∑ = 183.8 Mean = 7.658 ∑(X - )2 = SSx = 789.658 Y Values ∑ = 185.5 Mean = 7.729 ∑(Y - )2 = SSy = 376.43 X and Y Combined N = 24 ∑(X - )(Y - ) = 157.519 R Calculation r = ∑((X - )(Y - )) / √((SSx)(SSy)) r = 157.519 / √((789.658)(376.43)) = 0.2889 r = 0.2889(pearsons correlation coefficient.)

(e) Yes, the data are ratio data.

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