Question

Do students in early morning classes do more poorly than students in later classes? During one semester of Quan 2010, exam scores were averaged for one section of 28 students who met at 8:00am, and for another section of 37 students who met at 10:50am. The earlier section had a mean score of 80.6 with a variance of 103, while the later section had a mean score of 81.5 with a variance of 138.   

At a significance level of 0.10 can we conclude that 8:00am sections score lower than sections that meet at 10:50am?

Answer 1

Ho :   µ1 - µ2 =   0                  
Ha :   µ1-µ2 <   0                  
                          
Level of Significance ,    α =    0.1                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   80.60                  
standard deviation of sample 1,   s1 =    10.15                  
size of sample 1,    n1=   28                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   81.50                  
standard deviation of sample 2,   s2 =    11.75                  
size of sample 2,    n2=   37                  
                          
difference in sample means =    x̅1-x̅2 =    80.6000   -   81.5   =   -0.90  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    11.0905                  
std error , SE =    Sp*√(1/n1+1/n2) =    2.7780                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -0.9000   -   0   ) /    2.78   =   -0.32
                          
Degree of freedom, DF=   n1+n2-2 =    63                  

p-value =        0.373515   [ excel function: =T.DIST(t stat,df) ]              
Conclusion:     p-value>α , Do not reject null hypothesis                      
                          
There is not enough evidence to that 8:00am sections score lower than sections that meet at 10:50am

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