Question

Use the following information regarding a variable (Y) and a variable (X) to answer the next...

  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

Homework Answers

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

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