Question

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 negative 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	14
4	14
5	25
6	22
7	27
8	18
9	33
10	26
11	36
12	22

Ho: ρ = 0
Ha: ρ < 0

Find the Linear Correlation Coefficient
r =

Find the p-value
p-value =

Answer 1

The linear correlation coefficient is given by

= 0.6393

degrees of freedom = n-2 =8

P value = 0.0233 ( using P value calculator)

If we use r critical value table (one tailed ) we find

0.025 < P value < 0.05

Since P value > 0.01

We fail to reject H0

There is not sufficient evidence to conclude that correlation exists between advertising cost and profit .

Calculation

	x	y	x^2	y^2	xy
	3	14	9	196	42
	4	14	16	196	56
	5	25	25	625	125
	6	22	36	484	132
	7	27	49	729	189
	8	18	64	324	144
	9	33	81	1089	297
	10	26	100	676	260
	11	36	121	1296	396
	12	22	144	484	264
total	75	237	645	6099	1905