First year students Mean 125 SD size 350 Third year students

First year students: Mean 125, SD?, size 350

Third year students: Mean 112, SD?, size 150

Significance level = 0.02

Solution

Let

group 1 = first year
group 2 = third year

Formulating the hypotheses          
Ho: p1^ - p2^   >=   0  
Ha: p1^ - p2^   <   0  
Here, we see that pdo =    0   , the hypothesized population proportion difference.  
          
Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.357142857      
p2 = x2/n2 =    0.746666667      
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.043783715      
          
Thus,          
          
z = [p1 - p2 - pdo]/sd =    -8.896545395      
          
As significance level =    0.02   , then the critical z is  
          
zcrit =    -2.053748911      
          
Also, the p value is          
          
P =    2.8806E-19      
          
Thus comparing z and zcrit (or p and significance level), then we    REJECT THE NULL HYPOTHESIS.      
Thus, there is significant evidence that the proportion of third year students who buy used textbooks is greater than the proportion of first year student who buy used textbooks. [CONCLUSION]