Question

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 -9.17 12.12 9.17 26.43 Refer to above data. The sample correlation coefficient equals: a. .991 b. 1.67 c. .85 d. -0.94

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

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

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.

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

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

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

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

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

1. The conclusion is:

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

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

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

Answer 1

Given:

n = 8

∑ x = 56

∑ y = 296

∑ x2 = 428

∑ y2 = 11,920

∑ xy = 2,257

Now, = ∑x/ n = 56/8 = 7

= ∑y/n = 296/8 = 37

Reject H0 and conclude that a significant positive relation exists.