Question

Student #	Gender	Height	Shoe	Age	Hand
1	F	68	8.5	20	R
2	F	60	5.5	27	R
3	F	64	7	31	R
4	F	67	7.5	19	R
5	F	65	8	20	R
6	F	66	9	29	R
7	F	62	9.5	30	L
8	F	63	8.5	18	R
9	F	60	5	19	L
10	F	63	7.5	42	R
11	F	61	7	20	R
12	F	64	7.5	17	R
13	F	65	8	19	R
14	F	68	8	19	R
15	F	63	7.5	18	R
16	F	62	7.5	19	R
17	F	64	7	23	R
18	F	72	11	28	R
19	F	62	8	20	R
20	F	59	6.5	29	R
21	F	64	8.5	19	R
22	F	68	9.5	23	R
23	F	65	9.5	34	R
24	F	63	8	27	R
25	F	65	8	23	R
26	F	62	7.5	30	R
27	F	67	7.5	31	L
28	F	66	9	37	R
29	F	61	6	24	R
30	F	61	6.5	46	R
31	F	68	8	20	R
32	F	63	7.5	42	R
33	F	63	5.5	33	R
34	F	58	5	20	R
35	F	65	8	44	R
36	F	69	9	28	R
37	F	68	9	20	R
38	F	63	7	49	R
39	F	62	6.5	19	R
40	F	66	7.5	19	R
41	F	69	7.5	55	R
42	F	69	11	40	R
43	F	63	6.5	19	R
44	F	61	7.5	20	R
45	F	68	9	19	R
46	F	65	9	25	R
47	F	62	7	31	R

2. Using the SCC men’s/women’s class sample data at the ?=0.05, is there enough evidence to conclude that there is a significant linear correlation between men’s/women’s height and men’s/women’s shoe size?

a. State the null and alternate hypotheses.

b. Specify the level of significance.

c. State the correlation coefficient. (3 decimal places)

d. State the critical value from Table 11. (Use the value of n that is closest to your sample size.)

e. State whether to “reject the ?0” or “fail to reject the ?0”.

f. Interpret the decision in the context of the original claim

Answer 1

Let X: Height and Y: Shoe size

From given data, we have to construct below table to calculate correlation coefficient (r):

	Height (X)	Shoe (Y)	X2	Y2	X*Y
	68	8.5	4624	72.25	578
	60	5.5	3600	30.25	330
	64	7	4096	49	448
	67	7.5	4489	56.25	502.5
	65	8	4225	64	520
	66	9	4356	81	594
	62	9.5	3844	90.25	589
	63	8.5	3969	72.25	535.5
	60	5	3600	25	300
	63	7.5	3969	56.25	472.5
	61	7	3721	49	427
	64	7.5	4096	56.25	480
	65	8	4225	64	520
	68	8	4624	64	544
	63	7.5	3969	56.25	472.5
	62	7.5	3844	56.25	465
	64	7	4096	49	448
	72	11	5184	121	792
	62	8	3844	64	496
	59	6.5	3481	42.25	383.5
	64	8.5	4096	72.25	544
	68	9.5	4624	90.25	646
	65	9.5	4225	90.25	617.5
	63	8	3969	64	504
	65	8	4225	64	520
	62	7.5	3844	56.25	465
	67	7.5	4489	56.25	502.5
	66	9	4356	81	594
	61	6	3721	36	366
	61	6.5	3721	42.25	396.5
	68	8	4624	64	544
	63	7.5	3969	56.25	472.5
	63	5.5	3969	30.25	346.5
	58	5	3364	25	290
	65	8	4225	64	520
	69	9	4761	81	621
	68	9	4624	81	612
	63	7	3969	49	441
	62	6.5	3844	42.25	403
	66	7.5	4356	56.25	495
	69	7.5	4761	56.25	517.5
	69	11	4761	121	759
	63	6.5	3969	42.25	409.5
	61	7.5	3721	56.25	457.5
	68	9	4624	81	612
	65	9	4225	81	585
	62	7	3844	49	434
Total	= 3022	= 364.5	= 194736	= 2906.75	= 23572.5

Now, we have to compute correlation coefficient (r) using above table values, we get

  

a) State the null and alternative hypothesis:

= 0 (There is no correlation between X and Y)

0 (There is correlation between X and Y)

b) Specify level of significance ():

We have given,   = 0.05

c) State the correlation coefficient (r): We have already calculated using above table which is r = 0.735

d) Critical value:

Using = 0.05 and df = n-2 = 45, critical value is 0.288

e) decision rule: Here, r = 0.735 > 0.288, we reject the null hypothesis

f) Conclusion: We conclude that there is sufficient evidence to prove that there is correlation between Men's/Women's Height and Men's/women's Shoe size.