Question

The data below shows the annual salaries​ (in millions) and the number of viewers​ (in millions) of eight television actors and actresses. Answer parts ​a-c.

Salary​ (x)	97	12	13	33	11	7	8	2
	Viewers​ (y)	16	4.9	5.3	1.6	10.4	9.1	13.4		4.7

a. Find the value of the linear correlation coefficient r.

b. Find the critical values of r from the table showing the critical values for the Pearson correlation coefficient using alpha=0.05.

c. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Answer 1

Solution:

a)

	X	Y	XY	X2	Y2
	97	16	1552	9409	256
	12	4.9	58.8	144	24.01
	13	5.3	68.9	169	28.09
	33	1.6	52.8	1089	2.56
	11	10.4	114.4	121	108.16
	7	9.1	63.7	49	82.81
	8	13.4	107.2	64	179.56
	2	4.7	9.4	4	22.09
SUM	183	65.4	2027.20	11049	703.28

Putting values we get

r = 0.4938

b)

n = 8

df = n - 2 = 8 - 2 = 6

= 0.05

Using the critical value table for Pearson correlation coefficient, (two tailed )

Critical value are  0.707

c)

r = 0.4938

| r | = | 0.4938 | = 0.4938

r < 0.707

Fail to reject H₀

No significance correlation.

No sufficient evidence to conclude that there is a linear correlation between the two​ variables.