Question

The Director of Sales purposefully collected data on two variables. These variables are simply identified as Y and X. Data on these two variables are summarized in the table presented below.

Variable Y	Variable X
24 28 25	20 26 22
29 33 24 18 26 30 24 29 19	28 24 19 24 20 21 24 25 14

The Director approaches the Research Division for a validation of the speculative argument that ρ = 0, in the association involving Y and X.   The level of significance is 5%. Is it statistically true that ρ = 0? Show all the different stages of hypothesis testing and your calculations.

Answer 1

: population correlation coefficient

Null hypothesis : Ho : =0

Alternate hypothesis : H1 :

Two tailed test:

Test Statistic :

n : Number of pairs of observations : 12

	y	x	xy
	24	20	480	400	576
	28	26	728	676	784
	25	22	550	484	625
	29	28	812	784	841
	33	24	792	576	1089
	24	19	456	361	576
	18	24	432	576	324
	26	20	520	400	676
	30	21	630	441	900
	24	24	576	576	576
	29	25	725	625	841
	19	14	266	196	361
Total	=309	=267	=6967	=6095	=8169

r=0.5071

Value of the test statistic : t=1.8606;

Degrees of freedom = n-2 =12-2=10

p-value for two tailed test :

For 12 degrees of freedom

2P(t>1.8606) =2 x 0.0462=0.0924

p-value = 0.0924

Given level of significance : 5% i.e =0.02 ;

As p-value :0.0924 >  : 0.02; Fail to reject the null hypothesis.

There is not enough evidence to conclude that i.e

It is statistically true that =0