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 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 ​$60,000,000​, ​$91,000,000​, ​$48,000,000​, and so​ on? Budget​ (x) 60 91 48 40 196 100 87 Gross​ (y) 61 69 46 53 580 144 44

What are the null and alternative​ hypotheses?

A.

Upper H 0H0​:

rhoρnot equals≠0

Upper H 1H1​:

rhoρequals=0

B.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρnot equals≠0

C.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρgreater than>0

D.

Upper H 0H0​:

rhoρequals=0

Upper H 1H1​:

rhoρless than<0

Construct a scatterplot. Choose the correct graph below.

A.

02500800xy

A scatterplot has a horizontal x-scale from 0 to 250 in increments of 50 and a vertical y-scale from 0 to 800 in increments of 100. Seven points are plotted with approximate coordinates as follows: (40, 50); (50, 50); (60, 60); (85, 40); (90, 70); (100, 140); (195, 580).

B.

02500800xy

A scatterplot has a horizontal x-scale from 0 to 250 in increments of 50 and a vertical y-scale from 0 to 800 in increments of 100. Seven points are plotted with approximate coordinates as follows: (50, 410); (75, 400); (110, 220); (125, 300); (150, 200); (175, 300); (215, 200).

C.

02500800xy

A scatterplot has a horizontal x-scale from 0 to 250 in increments of 50 and a vertical y-scale from 0 to 800 in increments of 100. Seven points are plotted with approximate coordinates as follows: (50, 100); (75, 90); (110, 220); (125, 300); (150, 400); (175, 300); (215, 410).

D.

02500800xy

A scatterplot has a horizontal x-scale from 0 to 250 in increments of 50 and a vertical y-scale from 0 to 800 in increments of 100. Seven points are plotted with approximate coordinates as follows: (40, 650); (50, 610); (60, 710); (85, 550); (90, 660); (100, 600); (195, 100).

The linear correlation coefficient r is

nothing.

​(Round to three decimal places as​ needed.)

The test statistic t is

nothing.

​(Round to two decimal places as​ needed.)

The​ P-value is

nothing.

​(Round to three decimal places as​ needed.)

Because the​ P-value is

▼

greater

less

than the significance level

0.050.05​,

there

▼

is

is not

sufficient evidence to support the claim that there is a linear correlation between between budgets and gross receipts for a significance level of

alphaαequals=0.050.05.

Do the results change if the actual budgets listed are

​$60 comma 000 comma 00060,000,000​,

​$91 comma 000 comma 00091,000,000​,

​$48 comma 000 comma 00048,000,000​,

and so​ on?

A.

​Yes, the results would need to be multiplied by​ 1,000,000.

B.

​No, the results do not change because it would result in the same linear correlation coefficient.

C.

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

D.

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

Answer 1

a)

b)

Sl.No.	Budget (x)	Gross (y)	x^2	y^2	xy
1	60	61	3600	3721	3660
2	91	69	8281	4761	6279
3	48	46	2304	2116	2208
4	40	53	1600	2809	2120
5	196	580	38416	336400	113680
6	100	144	10000	20736	14400
7	87	44	7569	1936	3828
Total	622	997	71770	372479	146175
Average	88.85714	142.4286

Sxx	16500.86
Syy	230477.7
Sxy	57584.43

correlation coefficient r = = 0.934

H₀:

H₁:

alpha = 0.05

test statistic t = = 5.846

critical value = t_0.025,5 = 2.571

p-value = 0.00207 = 0.002

Because the​ P-value is less than the significance level 0.05​, there is a sufficient evidence to support the claim that there is a linear correlation between between budgets and gross receipts for a significance level of alpha =0.05.

c) if the actual budgets listed are ​$60,000,000​, ​$91,000,000​, ​$48,000,000​, and so​ on

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