Question

Use the following data:

x	y
10	3
6	7
9	3
3	8
2	9
8	5
3	7

1. Contract the scatter plot of these data. Describe relationship between x and y. What type of relationship appears to exist between two variables? (you can copy and past from Excel,SAS,etc)

2. Compute the correlation coefficient r.

3. Test to determine whether the population correlation coefficient is positive. Use the α=0.01 level to conduct test. (calculate test statistics and make conclusion)

Answer 1

a.

As 'x' increases y decreases; therefore '-' correlation:

n : Number of pairs of data = 7

	x	y	xy	x2	y2
	10	3	30	100	9
	6	7	42	36	49
	9	3	27	81	9
	3	8	24	9	64
	2	9	18	4	81
	8	5	40	64	25
	3	7	21	9	49
Total	= 41	=42	=202	=303	=286

Correlation coefficient : r

Correlation coefficient r = -0.95177852

Null hypothesis : Ho : Population Correlation coefficient = 0

Alternative hypothesis : Ho : Population Correlation coefficient > 0

Right tailed test

Right Tailed test :

Test Statistic

degrees of freedom = n-2 =7-2 =5

For Right tailed test :

For 5 degrees of freedom,

P(t>-6.9389) = 0.9995

Given, level of significnace , =0.01

As p-value is > level of significnace , (0.9995 > 0.01) Fail to reject the null hypothesis.

There is not sufficient evidence to conclude that there is positive correlation