Question

8. Listed below are the budgets​ (in millions of​ dollars) and the gross receipts​ (in millions of​ dollars) for randomly selected movies. 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 budgets and gross​ receipts? Do the results change if the actual budgets listed are ​$63000000. $85000000, $45000000, and so on

Budget_(x)         Gross_(y)

63           66

85           69

46           45

40           54

192         682

105         145

88           42

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 (less/greater) then the significant level 0.05, there (is/is not) evidence to support the claim that there is a linear correlation between budgets and gross receipts for a significance level of a=0.05

Does the results change if the actual budget listed are ​$63000000. $85000000, $45000000, and so on?

Yes, the results would change because it would result in a different correlation coefficient.

Yes, the results would need to be multiplied by 1000000

No, the results do not change because it would result in a different linear correlation coefficient

No, the result do not change it would result in the same linear correlation coefficient

Answer 1

	Budget X	Gross Y	X * Y
	63	66	4158	3969	4356
	85	69	5865	7225	4761
	46	45	2070	2116	2025
	40	54	2160	1600	2916
	192	682	130944	36864	465124
	105	145	15225	11025	21025
	88	42	3696	7744	1764
Total	619	1103	164118	70543	501971

To Test :-

H0 :-  

H1 :-  

Test Statistic :-


t = 5.423

Test Criteria :-
Reject null hypothesis if


Result :- Reject null hypothesis

Decision based on P value
P - value = P ( t > 5.423 ) = 0.003
Reject null hypothesis if P value <    level of significance
P - value = 0.003 < 0.05 ,hence we reject null hypothesis
Conclusion :- We reject H0

Because the P-value is (less) then the significant level 0.05, there (is/is not) evidence to support the claim that there is a linear correlation between budgets and gross receipts for a significance level of a=0.05

Does the results change if the actual budget listed are ​$63000000. $85000000, $45000000, and so on?

No, the result do not change it would result in the same linear correlation coefficient