Question

3. The College of Business would like to test if there is a positive relationship between GPA and starting monthly salary of its graduates. They ask 8 recent graduates their GPA and starting salaries and find that the correlation coefficient in the sample is 0.802. Test using α=0.05.

a. Set up the null and alternate hypotheses.

b. Calculate an appropriate test statistic.

c. What is the p-value? Explain your conclusion in the context of the question.

Answer 1

a)

Ho:   ρ = 0
Ha:   ρ > 0

b)

n=   8                          
alpha,α =    0.05                          
correlation , r =   0.8020                          
                              
Df =    n-2 =   6                      
t-test statistic = r*√(n-2)/√(1-r²) =        0.8020   * √    6   / √ ( 1 -    0.8020   ² ) =   3.289

c)

p-value =    0.9917   [excel function: =t-dist.rt(t-stat,df) ]   
decision:   p value > α , so, do not reject the null hypothesis      

there is no enough evidence to conlcude that there is a positive relationship between GPA and starting monthly salary of its graduates