Question

Results... The stem-and- In A Student Survey, Fifty-two P... Timelimit: 3 hours. [X] Show Intro/Instructions Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit. Use a significance level of 0.01 and round all values to 4 decimal places. Advertising Cost Profit 3 25 17 4 5 21 6 17 7 21 8 19 33 9 10 24 11 35 Ho: p=0 Ha: p=0 Find the Linear Correlation Coefficient Find the p-value p-value = The p-value is Greater than a Less than or equal to) a The p-value leads to a decision to Do Not Reject Ho Reject Ho % & 5 7 6 8 9 0 U Y 0 Р R

Answer 1

Here we have to test that

$H_0:\rho =0$

H, :ρ#0

Let x be the Amount spent on Advertising (in millinons of dollars)

and y be the Profit (in millions of dollars).

n = 9

x	y	x*y	T	$y^2$
3	25	75	9	625
4	17	68	16	289
5	21	105	25	441
6	17	102	36	289
7	21	147	49	441
8	19	152	64	361
9	33	297	81	1089
10	24	240	100	576
11	35	385	121	1225
α = 63	$\sum y=212$	$\sum x*y=1571$	$\sum x^2=501$	g = 5336

Linear Correlation Coefficient (r) :

$r=\frac{(n*\sum x*y)-(\sum x*\sum y)}{\sqrt{[(n*\sum x^2)-(\sum x)^2]*[(n*\sum y^2)-(\sum y)^2]}}$

$r=\frac{(9*1571)-(63*212)}{\sqrt{[(9*501)-(63)^2]*[(9*5336)-(212)^2]}}$

$r=\frac{14139-13356}{\sqrt{[4509-3969]*[48024-44944]}}$

$r=\frac{783}{\sqrt{8478*92968}}$

$r=\frac{783}{\sqrt{788182704}}$

$r=\frac{783}{28074.592}$

r = 0.0279 (Round to 4 decimal)

Linear Correlation coefficient = 0.0279

Test statistic:

$t=\frac{r*\sqrt{n-2}}{\sqrt{1-r^2}}$

$t=\frac{0.0279*\sqrt{9-2}}{\sqrt{1-0.0279^2}}$

$t=\frac{0.0279*\sqrt{7}}{\sqrt{1-0.000778}}$

$t=\frac{0.0279*2.645751}{\sqrt{0.999222}}$

$t=\frac{0.073816}{\sqrt{0.999222}}$

$t=\frac{0.073816}{0.999611}$

t = 0.074 (Round to 3 decimal)

Test statistic = t = 0.074

Test is two tailed test.

Degrees of freedom = n - 2 = 9 - 2 = 7

Level of significance = $\alpha$ = 0.01

P value from excel using function:

=0.9431 (Round to 4 decimal)

P value = 0.9431

The p value is greater than $\alpha$

The p -value leads to a decision to Do not reject H0.

The conclusion is

There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit.