Suppose that the test scores in two classes were collected a

Suppose that the test scores in two classes were collected, and data was summarized as follows: Class I n=16 mean = 78.9 S = 9 Class II n=16 mean = 84.7 S = 7. Assuming the populations\' variances are equal, test, at the 0.05 level of significance, if there is a difference between the two means of the classes, by showing all the steps and information needed in the calculations.

Solution

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    78.9          
X2 =    84.7          
              
Calculating the standard deviations of each group,              
              
s1 =    9          
s2 =    7          
              
Thus, the pooled standard deviation is given by              
              
S = sqrt[((n1 - 1)s1^2 + (n2 - 1)(s2^2))/(n1 + n2 - 2)]               
              
As n1 =    16   , n2 =    16  
              
Then              
              
S =    8.062257748          
              
Thus, the standard error of the difference is              
              
Sd = S sqrt (1/n1 + 1/n2) =    2.850438563          
              
As ud = the hypothesized difference between means =    0   , then      
              
t = [X1 - X2 - ud]/Sd =    -2.034774605          
              
Getting the critical value using table/technology,              
df = n1 + n2 - 2 =    30          
tcrit =    +/-   2.042272456      
              
Getting the p value using technology,              
              
p =    0.050794301          
              
As |t| < 2.0422, and P > 0.05, we   FAIL TO REJECT THE NULL HYPOTHESIS.          

Thus, there is no significant evidence that there is a difference between the two means of the classes. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this two tailed test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!