Question

Peter put forth a hypothesis that “One’s Income is Positively Related to Education”. Income was measured by the amount of income one got each month while education was measured by the number of years of formal education one had received. (50%)

He found that Pearson r = 0.02, and the significance level (p) = 0.15.

1. Should he reject or confirm his hypothesis? Why or why not?

2. Could he use chi square in this instance? Why or why not? '

3. If he wants to use T-test, what he should do with the data?

4. Is it appropriate to use regression analysis to test his hypothesis? Why or why not?

5. What are the two most important coefficients in constructing a regression equation?

Answer 1

Here our hypothesis is

H0: There is no relation between Income and education (r=0).
H1: Income is Positively Related to Education (r>0)

1. Since he got P=0.15 and it is greater than the 0.05 thus the null hypothesis can not be rejected. That is there is not significant evidence that Income is Positively Related to Education.

2. He should not use chi square test since it is used to determine if there is a significant relationship between two nominal (categorical) variables and here our variables are quantative (since it is given that Income was measured by the amount of income one got each month while education was measured by the number of years of formal education one had received ).

3. If he want to use t-test than he should check by appropriate meathods (probability ploting) that if the data follow normal distibution.

4. Yes we can use regression analysis to test his hypothesis by consedring following.

Suppose

Y denotes the income and X denotes the education. So if he test the hypothesis

than he can fulfill his goal, since represents the relation between X and Y.

5. As in part 4 the two most important coefficints are the intercept and slope .