Question

f you are male, use the men’s heights and shoe sizes as your data.

If you are female, use the women’s heights and shoe sizes as your data.

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

1. NOTE: Be sure to use the original, unsorted data for this problem.

Make a scatterplot on your calculator using the men’s/women’s heights as the x-variable and men’s/women’s shoe size as y-variable.

a. Is there an increasing or decreasing pattern? Explain what that means in terms of height and shoe sizes.

b. Calculate the correlation coefficient, r. (3 decimal places)

c. Calculate the regression equation. (Round to 3 decimal places.)

d. Use the equation to predict the shoe size (to nearest ½ size) for a man/woman who is 5 feet 7 inches tall.

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

30	F	61	6.5	46	R		R Square	0.540241231
31	F	68	8	20	R		Adjusted R Square	0.53002437
32	F	63	7.5	42	R		Standard Error	0.903712776
33	F	63	5.5	33	R		Observations	47
34	F	58	5	20	R
35	F	65	8	44	R		ANOVA
36	F	69	9	28	R			df	SS	MS	F	Significance F
37	F	68	9	20	R		Regression	1	43.18481503	43.18481503	52.87741545	4.03648E-09
38	F	63	7	49	R		Residual	45	36.75135518	0.816696782
39	F	62	6.5	19	R		Total	46	79.93617021
40	F	66	7.5	19	R
41	F	69	7.5	55	R			Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
42	F	69	11	40	R		Intercept	-12.673	2.812348305	-4.50609809	4.6669E-05	-18.33707758	-7.008357074	-18.33707758	-7.008357074
43	F	63	6.5	19	R		Height	0.318	0.043691295	7.271685874	4.03648E-09	0.229710585	0.405708154	0.229710585	0.405708154
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

The scatter plot between men’s/women’s heights and men’s/women’s shoe size is given below,

1. The scatter plot shows there is an increasing pattern between the variables indicating that as the height increases so as the shoe size.
2. The calculated correlation coefficient is 0.735.
3. The obtained regression equation is,

Shoe Size = -12.673+0.318*Height

4. Using the above equation the predicted shoe size (to nearest ½ size) for a man/woman who is 5 feet 7 inches tall is,

Shoe Size = -12.673+0.318*(5*12+7) = 8.63 = 8.5