Question

In a survey of 735 students at North Campus, the mean GPA of foreign-born students was found to be 3.234 with a standard deviation of 0.047. Using these results, test the claim at the .05 significance level that the mean GPA of foreign-born students at North Campus is equal to 3.00. Be sure to show all the steps in the hypothesis testing procedure including the claim, the null and alternative hypotheses, the calculation of the test statistic, the p-value, your decision to reject the null hypothesis or not, and correct wording of the final conclusion.

Answer 1

Ho :   µ =   3                  
Ha :   µ ╪   3       (Two tail test)          
                          
Level of Significance ,    α =    0.050                  
sample std dev ,    s =    0.0470                  
Sample Size ,   n =    735                  
Sample Mean,    x̅ =   3.2340                  
                          
degree of freedom=   DF=n-1=   734                  
                          
Standard Error , SE = s/√n =   0.0470   / √    735   =   0.0017      
t-test statistic= (x̅ - µ )/SE = (   3.234   -   3   ) /    0.0017   =   134.978
                          
  
p-Value   =   0.0000   
Decision:   p-value<α, Reject null hypothesis                       
Conclusion: There is enough evidence to conclude that the mean GPA of foreign-born students at North Campus is not equal to 3.00