Question

12. The data below shows the annual salaries​ (in millions) and the number of viewers​ (in millions) of eight television actors and actresses. Construct a​ scatterplot, find the value of the linear correlation coefficient​ r, and find the​ P-value using a=0.05. Is there sufficient evidence to conclude that there is a linear correlation between the two​ variables?

Salary_(x)            Viewers_(y)

91           17

13           4.7

15           5.3

30           1.5

10           10.6

5              9.8

7              13.2

4              4.6

Construct the scatterplot.

The linear correlation coefficient r is _____

(Round to three decimal places as​ needed.)

The test statistic t is _____

(Round to three decimal places as​ needed.)

The​ P-value is ______

(Round to three decimal places as​ needed.)

Because the​ P-value is (greater,less) than the significance level 0.05​, there (is not, is) sufficient evidence to support the claim that there is a linear correlation between selling price​ (in hundred​ thousands) and the list price​ (in hundred​ thousands) of homes sold for a significance level of a=0.05.

Answer 1

	X	Y	X * Y
	91	17	1547	8281	289
	13	4.7	61.1	169	22.09
	15	5.3	79.5	225	28.09
	30	1.5	45	900	2.25
	10	10.6	106	100	112.36
	5	9.8	49	25	96.04
	7	13.2	92.4	49	174.24
	4	4.6	18.4	16	21.16
Total	175	66.7	1998.4	9765	745.23

To Test :-

H0 :-

H1 :-  

Test Statistic :-


t = 1.448

Test Criteria :-
Reject null hypothesis if

-2.4469 < 1.4485 < 2.4469
Result :- We fail to Reject null hypothesis

Decision based on P value
P - value = P ( t > 1.4485 ) = 0.198
Reject null hypothesis if P value <    level of significance
P - value = 0.1976 > 0.05 ,hence we fail to reject null hypothesis
Conclusion :- We Accept H0

There is statistically uncorrelation between two variables at 5% level of significance.

Because the​ P-value is (greater) than the significance level 0.05​, there (is not ) sufficient evidence to support the claim that there is a linear correlation between selling price​ (in ​ thousands) and the list price​ (in ​ thousands) of homes sold for a significance level of a=0.05.