Question

Use the given data set to complete parts (a) through (c) below. (Use a-0.05.) 10 9.13 13 8.75 12 9.13 3.11 4.74 8.14 8.77 9.25 8.09 6.13 7.25 Click here to view a table of critical values for the correlation coefficient. a. Construct a scatterplot. Choose the correct graph below. OA. OB. O C. OD. 12 16 12 16 8 12 16 12 16 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.)

Answer 1

a)

Scatterplot 10 6 4 0 16 14 12 10 6 4 2 0

so, option d) is correct

b)

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
10	9.13	1.000	2.660	1.631
8	8.14	1.000	0.411	-0.641
13	8.75	16.000	1.565	5.004
9	8.77	0.000	1.615	0.000
11	9.25	4.000	3.066	3.502
14	8.09	25.000	0.349	2.955
6	6.13	9.000	1.874	4.107
4	3.11	25.000	19.264	21.945
12	9.13	9.000	2.660	4.893
7	7.25	4.000	0.062	0.498
5	4.74	16.000	7.613	11.036

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	99	82.49	110.000	41.1	54.93
mean	9.00	7.50	SSxx	SSyy	SSxy

correlation coefficient , r = Sxy/√(Sx.Sy)   =0.817

-----------------

correlation hypothesis test

Ho:ρ = 0

Ha:ρ ╪ 0

n=11

alpha,α = 0.05

correlation , r=0.8166

t-test statistic = t = r*√(n-2)/√(1-r²) = 4.244

p-value = 0.0022

p-value <α=0.05,reject Ho

so, answer is

there is sufficient evidence to support the claim of a linear correlation