Question

1. Use the following information regarding a variable (Y) and a variable (X) to answer the next 7 questions.
   
   n = 8           
   ∑ x = 56
   ∑ y = 296
   ∑ x ² = 428
   ∑ y ² = 11,920
   ∑ xy = 2,257
   
   The sample covariance equals

   		26.43
   		-9.17
   		9.17
   		12.12

3 points   

QUESTION 23

1. Refer to above data.
   
   The sample correlation coefficient equals:

   	a.	-0.94
   	b.	1.67
   	c.	.991
   	d.	.85

3 points   

QUESTION 24

1. Given the sample correlation coefficient in above question, the comment is:

   	a.	There is a strong and positive relation between X & Y.
   	b.	There is a weak and positive relation between X & Y.
   	c.	There is a strong and negative relation between X & Y.
   	d.	Not enough information to comment.

3 points   

QUESTION 25

1. Refer to above question.
   
   To test for a direct relation between X and Y, the appropriate hypothesis is:

   	a.	Ho: ρ < 0 Ha: ρ > 0
   	b.	Ho: ρ = 0 Ha: ρ ≠ 0
   	c.	Ho: ρ > 0 Ha: ρ < 0
   	d.	Ho: ρ = 0 Ha: ρ > 0

3 points   

QUESTION 26

1. For the above test, the calculated value of test statistic is:

   	a.	-2.55
   	b.	-4.55
   	c.	17.51
   	d.	3.61

3 points   

QUESTION 27

1. Using a 1% significance level, the critical value for this test is:

   	a.	3.143
   	b.	1.812
   	c.	2.015
   	d.	1.796

2 points   

QUESTION 28

1. The conclusion is:

   	a.	Reject H0 and conclude that a significant positive relation exists.
   	b.	Reject H0 and conclude that a significant negative relation exists.
   	c.	Fail to reject H0 and conclude that no relation exists.
   	d.	Fail to reject H0 and conclude that a negative relation exists.

2 points   

QUESTION 29

1. Which of the following values for r (sample correlation coefficient) exhibits the least relationship?

   	a.	+0.18
   	b.	-0.21
   	c.	-0.01
   	d.	-0.80
   	e.	-0.99

Answer 1

n=		8
Σx=		56
Σx2 =		428
Σy =		296
Σy2 =		11920
Σxy=		2257
SSx=Σx2-(Σx)2/n=		36
SSy=Σy2-(Σy)2/n=		968
SP=Σxy-(ΣxΣy)/n=		185

22)sample covariance =SP/(n-1) =185/7 =26.43

23)

sample correlation coefficient r=SP/(√SSx*Ssy)=

0.991

24)

There is a strong and positive relation between X & Y.

25)

Ho: ρ = 0 Ha: ρ > 0

26)

calculated value of test statistic =r*sqrt((n-2)/(1-r^2))=17.51

27)

Using a 1% significance level, the critical value for this test is =3.143

28)

Reject H0 and conclude that a significant positive relation exists.

29)Which of the following values for r (sample correlation coefficient) exhibits the least relationship?

-0.01