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 alphaequals0.05. 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 ​$65 comma 000 comma 000​, ​$89 comma 000 comma 000​, ​$51 comma 000 comma 000​, and so​ on? Budget​ (x) 65 89 51 35 204 98 85

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Question :

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 alpha = 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 $61,000,000, $92,000,000, $48,000,000, and so onBudget(x) 61 92 48 36 135 58 93Gross(y) 69 62 53 58 627 144 42

a. What are the null and alternative hypotheses?i) H_0: rho = 0, H_1: rho < 0

ii) H_0: rho = 0, H_1: rho notequalto 0

iii) H_0: rho notequalto 0, H_1: rho = 0

iv) H_0: rho = 0, H_1: rho > 0

b. Construct a scatterplot. Choose the correct graph below.

c. The linear correlation coefficient r is.

d. The test statistic t is.

e. The P-value is.

Pvalue > α ; Hence, we fail to reject the null.

Step-by-step explanation:

When testing for correlation :

Correlation Coefficient r is always between - 1 and 1. The alternative is always the opposite of the null. To claim that correlation exists, the r will not be equal to 0, because 0 means no correlation.

1.)

H_0: rho = 0,

H_1: rho notequalto 0

2.)

Given the data :

Budget(x) : 61 92 48 36 135 58 93

Gross(y) : 69 62 53 58 627 144 42

Scatter plot is attached below

3.) The linear correlation Coefficient as obtained using technology is 0.751 ; which depicts a strong positive correlation

4.)

Test statistic :

T = r / √(1 - r²) / (n - 2)

r² = 0.751² = 0.564

T = 0. 751 / √(1 - 0.564) / (7 - 2)

T = 0.751 / 0.2952964

T = 2.543

E.)

Using the Value from Tscore calculator :

Pvalue(2.543, 5) ; two tailed

Pvalue = 0.0517

At α = 0.05;

Pvalue > α ; Hence, we fail to reject the null. there is no sufficient evidence to conclude that there is a linear correlation between budgets and gross receipts.

i dont know

step-by-step explanation:

7. d. 64

8. i. 32

9. c. 125

10. j. none of the above

11. d. 81

12. i. 216

13. e. none of the above

14. g. 240

15. e. none of the above

16. g. 32

17.   e. none of the above