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

alphaαequals=0.050.05.

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 00065,000,000​,

​$86 comma 000 comma 00086,000,000​,

​$53 comma 000 comma 00053,000,000​,

and so​ on?

Budget​ (x)	6565	8686	5353	3232	203203	103103	9393
Gross​ (y)	6969	6262	4848	5656	513513	143143	4747

What are the null and alternative​ hypotheses?

Construct a scatterplot

The linear correlation coefficient r is

The test statistic t is

The​ P-value is

Because the​ P-value is ____ (greater or less) than the significance level 0.05 there ____ (is or 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 α=0.05

Do the results change if the actual budgets listed are $65,000,000 $86,000,000​, ​$53,000,000​, and so​ on? (options listed below)

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

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

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

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

Answer 1

Please check the given data is the same or not as your data values are repeated twice. Please do the comment I will edit my answer if there is any change.

Budget(x)	Gross(y)
65	69
86	62
53	48
32	56
203	513
103	143
93	47

What are the null and alternative​ hypotheses?

HO:p=0

H1:p not equal to 0

Construct a scatterplot

The linear correlation coefficient r is 0.926

The test statistic t is 30.058

The​ P-value is 0.003

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

Do the results change if the actual budgets listed are $65,000,000 $86,000,000​, ​$53,000,000​, and so​ on? (options listed below)

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

..................................................................................................................................................................................

Regression Analysis
	r²	0.857
	r	0.926
	Std. Error	70.486
	n	7
	k	1
	Dep. Var.	Gross(y)
ANOVA table
Source	SS	df	MS	F	p-value
Regression	1,49,338.6036	1	1,49,338.6036	30.058	.0028
Residual	24,841.3964	5	4,968.2793
Total	1,74,180.0000	6
Regression output				confidence interval
variables	coefficients	std. error	t (df=5)	p-value	95% lower	95% upper
Intercept	-125.0177
Budget(x)	2.8553	0.5208	5.483	.0028	1.5166	4.1941