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

equals0.05.

Budget_(x)   Gross_(y)
61   66
88   69
53   51
40   56
203   598
101   141
85   48

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 comma 000 comma 000

,

$88 comma 000 comma 000

,

$53 comma 000 comma 000

,

and so on?

What are the null and alternative hypotheses?

Construct a scatterplot. Choose the correct graph below.

The linear correlation coefficient r is

(Round to three decimal places as needed.)

The test statistic t is

(Round to two decimal places as needed.)

The P-value is

(Round to three decimal places as needed.)

Because the P-value is

▼

greater

less

then the significance level

0.05

,

there

▼

is

is not

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

alpha

equals0.05

.

Do the results change if the actual budgets listed are

$61 comma 000 comma 000

,

$88 comma 000 comma 000

,

$53 comma 000 comma 000

,

and so on?

A.

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

B.

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

C.

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

D.

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

ASAP

Answer 1

a) Scatter Plot

b) Correlation Coefficient

The Correlation Coefficient is r = 0.947

c) Hypothesis Testing

Null Hypothesis $H0: \rho =0$

ALternative Hypothesis $H1: \rho \neq 0$

Under H0, the test statistic is

$t = \frac{r\sqrt{n-2}}{\sqrt{1-r^2}} =\frac{0.9465\sqrt{5}}{\sqrt{1-0.9465^2}}=6.56$

Degrees of Freedom = n-2 = 5

Significance Level $\alpha = 0.05$

The p value is 0.001

Answer: Because the P-value is less then the significance level 0.05 there is sufficient evidence to support the claim that there is a linear correlation between budgets and gross receipts for a significance level of $\alpha = 0.05$

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