A STAT 200 instructor is interested in whether there is any

A STAT 200 instructor is interested in whether there is any variation in the final exam grades between her two classes Data collected from the two classes are as follows:

Section 1: n1=28 x1= 80 s1=16

Section 2: n2=25 x2= 75 s2= 12

(a) Determine the test statistic.

(b) Determine the P-value for this test.

(c) Is there sufficient evidence to justify the rejection of 0 H at the significance level of 0.05?
Explain.

Solution

A)

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 =    80          
X2 =    75          
              
Calculating the standard deviations of each group,              
              
s1 =    16          
s2 =    12          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    28          
n2 = sample size of group 2 =    25          
Thus, df = n1 + n2 - 2 =    51          
Also, sD =    3.860421887          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    1.295195227   [ANSWER, TEST STATISTIC]      

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B)
              
Also, using p values,   as df = 51,          
              
p =    0.201085366   [ANSWER, P VALUE]      
              
c)

Comparing p > 0.05,    WE FAIL TO REJECT THE NULL HYPOTHESIS.          
              
Thus, there no sufficient evidence to justify the rejection of Ho at the significance level of 0.05.