Question

II. A study was done to test whether the amount of narcissism (Y) on number of friends (X) someone has. A sample of 10 participants was used. Both variables are numeric. The only other data that you have is that r = .4 and SS_Y = 60. Assume an alpha level of .05.

9. What statistical test should you use to evaluate the hypothesis above?

1. one-way independent ANOVA
2. simple linear regression
3. Pearson Product Moment Correlation

10. What are the null and alternative hypotheses in words?

Null hypothesis:

Alternative hypothesis: Th

11. What is the critical value?

12. Knowing that r = .4 and SS_Y = 60, calculate the appropriate test statistic (r or F).

14. Can you reject the null? No

Problem II. A study was done to investigate if time management skills is a good predictor of college grade point average (GPA). A sample of 57 participants was used. Assume an alpha level of .05.

1.1 State the null and alternative hypotheses (0.5 point)

Null hypothesis: There is no relationship between time management skills and GPA

Alternative hypothesis: There is a relationship between time management skills and GPA

1.2 What is the correct statistical test to evaluate the hypothesis? (0.5 point)

Simple linear regression

1.3 Calculate the appropriate test statistic given that SS_y = 20.6 and r = .5. (4 points)

1.4 What is the standard error? (1 point)

standard error =

1.5 Find critical F (0.5 points)

1.6 What is your conclusion? Specifically, state if there is any significance and what is your decision regarding the null hypothesis (0.5 points)

Answer 1

Problem 1:

9. Option: 2. simple linear regression

10. Null hypothesis: X and Y are not linearly related.

Alternative hypothesis: X and Y are linearly related.

11. Critical value=F_0.05,1,8=5.3177 (R code: qf(1-0.05,1,8))

12. Given r = .4 and SS_Y = 60,

The appropriate test statistic, F= [r²/(1-r²)]*(8/1)=8*0.4^2/(1-0.4^2)=1.5238.

14. No, Since Value of F<Critical value.

Problem II. A study was done to investigate if time management skills is a good predictor of college grade point average (GPA). A sample of 57 participants was used. Assume an alpha level of .05.

1.1 Null hypothesis: There is no relationship between time management skills and GPA

Alternative hypothesis: There is a relationship between time management skills and GPA

1.2 Simple linear regression

1.3 Given SS_y = 20.6 and r = .5. (4 points)

Value of test statistic=F= [r²/(1-r²)]*(55/1)=55*0.5^2/(1-0.5^2)=18.3333

1.4

1.5 Critical F=F_0.05,1,55=4.0162 (R code: qf(1-0.05,1,55))

1.6 Since Value of test statistic>Critical F, we reject null hypothesis at 5% level of significance and conclude that there is a significance linear relation between these two variables.