Question

Use the given data set to complete parts​ (a) through​ (c) below.​ (Use

alphaαequals=​0.05.)

x	10	8	13	9	11	14	6	4	12	7	5
y	9.14	8.13	8.73	8.78	9.25	8.11	6.12	3.11	9.12	7.26	4.73

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Click here to view a table of critical values for the correlation coefficient.

a. Construct a scatterplot. Choose the correct graph below.

A.

04812160246810xy

A scatterplot has a horizontal x-scale from 0 to 16 in increments of 2 and a vertical y-scale from 0 to 10 in increments of 1. Eleven points are plotted with approximate coordinates as follows: (4, 3.2); (5, 4.8); (6, 6.2); (7, 7.2); (8, 8.2); (9, 8.8); (10, 9.2); (11, 9.2); (12, 9.2); (13, 8.8); (14, 8.2).

relation​ coefficient, r, then determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables.

The linear correlation coefficient is

r=?

​(Round to three decimal places as​ needed.)

Answer 1

Following is the scatter plot:

(b)

Following table shows the calculations:

	X	Y	X^2	Y^2	XY
	10	9.14	100	83.5396	91.4
	8	8.13	64	66.0969	65.04
	13	8.73	169	76.2129	113.49
	9	8.78	81	77.0884	79.02
	11	9.25	121	85.5625	101.75
	14	8.11	196	65.7721	113.54
	6	6.12	36	37.4544	36.72
	4	3.11	16	9.6721	12.44
	12	9.12	144	83.1744	109.44
	7	7.26	49	52.7076	50.82
	5	4.73	25	22.3729	23.65
Total	99	82.48	1001	659.6538	797.31

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Conclusion; There is sufficient evidence to support the claim of a linear correlation between the two variables.