Question

Use the given data set to complete parts (a) through (c) below. (Use α = 0.05.) 

x	10	8	13	9	11	14	6	4	12	7	5
y	9.14	8.15	8.74	8.77	9.27	8.11	6.12	3.09	9.14	7.25	4.73

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

b. Find the linear correlation 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.) 

Using the linear correlation coefficient found in the previous step, determine whether there is sufficient evidence to support the claim of a linear correlation between the two variables. Choose the correct answer below.

A. There is sufficient evidence to support the claim of a nonlinear correlation between the two variables. 

B. There is insufficient evidence to support the claim of a linear correlation between the two variables. 

C. There is insufficient evidence to support the claim of a nonlinear correlation between the two variables. 

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

c. Identify the feature of the data that would be missed if part (b) was completed without constructing the scatterplot. Choose the correct answer below. 

A. The scatterplot reveals a distinct pattern that is not a straight-line pattern. 

B. The scatterplot reveals a distinct pattern that is a straight-line pattern with negative slope. 

C. The scatterplot does not reveal a distinct pattern. 

D. The scatterplot reveals a distinct pattern that is a straight-line pattern with positive slope.

Answer 1

a) Scatter plot

b)

Sl.No.	x	y	(x - bar{x})(y-bar{y})
1	10	9.14	1.639
2	8	8.15	-0.649
3	13	8.74	4.956
4	9	8.77	0.000
5	11	9.27	3.538
6	14	8.11	3.045
7	6	6.12	4.143
8	4	3.09	22.055
9	12	9.14	4.917
10	7	7.25	0.502
11	5	4.73	11.084
Sum	99	82.51	55.230
Average	9	7.501
Std dev	Sx = 3.317	Sy = 2.038

covariance = sum ((x - bar{x})(y-bar{y}))/(n-1) = 55.230/10 = 5.523

Linear correlation coefficient r = covariance/(Sx*Sy)

Linear correlation coefficient r = 0.817

critical value for n-2 df (9) and alpha 0.05 =0.602

we reject null hypothesis

there is a sufficient evidence to support the claim of linear correlation between the two variables.

c) The scatter plot reveals a distinct pattern that is not a straight line.