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 42a. What are the null and alternative hypotheses?i) H_0: rho = 0, H_1: rho < 0ii) H_0: rho = 0, H_1: rho notequalto 0iii) H_0: rho notequalto 0, H_1: rho = 0iv) H_0: rho = 0, H_1: rho > 0b. 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.

The answers are below

Step-by-step explanation:

1. H0: rho = 0

  H1: rho not equal to 0

2. I will add the scatter plot as an attachment

3. ΣX = 523,

ΣY = 1055

ΣX² = 46023

ΣY²= 430407

ΣXY = 111448

n = 7

The correlation coefficient r =

r = 7(111448)-(523)(1055)/√7(46023)-(523)² × √7(430407)-(1055)²

r = 780136-551765/√322161-273529√3012849-1113025

= 228371/220.53*1378.34

= 228371/303965.32

r = 0.751

4. Test statistics

t = r√n-2/√1-r²

= 0.751√5/√0.5640

= 1.679/0.660

= 2.543

5. P value

Degrees of freedom n-2 = 5

T dist(2.543,5,2)

The p value is less than 0.05 so we reject null hypothesis. There is enough evidence to show a linear correlation between budgets and gross receipts.

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{x = -1/2 ,   y = -1

step-by-step explanation:

solve the following system:

{2 x + y = -2

{10 x - 3 y = -2

in the first equation, look to solve for y:

{2 x + y = -2

{10 x - 3 y = -2

subtract 2 x from both sides:

{y = -2 x - 2

{10 x - 3 y = -2

substitute y = -2 x - 2 into the second equation:

{y = -2 x - 2

{10 x - 3 (-2 x - 2) = -2

10 x - 3 (-2 x - 2) = (6 x + 6) + 10 x = 16 x + 6:

{y = -2 x - 2

{16 x + 6 = -2

in the second equation, look to solve for x:

{y = -2 x - 2

{16 x + 6 = -2

subtract 6 from both sides:

{y = -2 x - 2

{16 x = -8

divide both sides by 16:

{y = -2 x - 2

{x = -1/2

substitute x = -1/2 into the first equation:

{y = -1

{x = -1/2

collect results in alphabetical order:

answer:   {x = -1/2 ,   y = -1