Do men score lower on average compared to women on their statistics finals? Final exam scores...

we will use t test for two independent samples

Ho :   µ1 - µ2 =   0 or µ1 =µ2
Ha :   µ1-µ2 <   0 or µ1<µ2

Sample #1   ---->   1
mean of sample 1,    x̅1=   74.417
standard deviation of sample 1,   s1 =    9.307
size of sample 1,    n1=   12
      
Sample #2   ---->   2
mean of sample 2,    x̅2=   83.083
standard deviation of sample 2,   s2 =    9.376
size of sample 2,    n2=   12

b)

difference in sample means =    x̅1-x̅2 =    74.4167   -   83.1   =   -8.667  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    9.3416                  
std error , SE =    Sp*√(1/n1+1/n2) =    3.8137                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   -8.6667   -   0   ) /    3.81   =   -2.27

c)

Degree of freedom, DF=   n1+n2-2 =    22  
p-value =        0.0166 [ excel function: =T.DIST(t stat,df) ]

d)

p value is greater than α

e) should not reject

f) the result are not statiscally significant....,so there is not sufficient evidence...............