A Troy University professor wanted to study how students from two campuses compa

Question

A Troy University professor wanted to study how students from two campuses compared in their capabilities of using Excel spreadsheets in Statistics courses. One campus is in Montgomery and the other campus is in Troy. The following table contains information regarding the years of spreadsheet usage of the students:

School

Sample Size

Sample Mean

(year)

Sample Standard

Deviation (year)

Troy

72

3.8

0.8

Montgomery

61

4.5

1.2

Using a 0.01 level of significance, is there evidence of the population means in years of spreadsheet usage of students at Montgomery campus longer than Troy campus?

Assume different population standard deviations.

School

Sample Size

Sample Mean

(year)

Sample Standard

Deviation (year)

Troy

72

3.8

0.8

Montgomery

61

4.5

1.2

Explanation / Answer

Let

u1 = population mean of Montgomery
u2 = population mean of Troy

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   <=   0  
Ha:   u1 - u2   >   0  

At level of significance =    0.01          

As we can see, this is a    right   tailed test.      
Calculating the means of each group,              
              
X1 =    4.5          
X2 =    3.8          
              
Calculating the standard deviations of each group,              
              
s1 =    1.2          
s2 =    0.8          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    61          
n2 = sample size of group 2 =    72          
Thus, df = n1 + n2 - 2 =    131          
Also, sD =    0.180264934          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    3.883173428          
              
where uD = hypothesized difference =    0          
              
Now, the critical value for t is              
              
tcrit =        2.355150397      
              
Also, using p values,              
              
p =    8.13753E-05          
              
As t > 2.355, and P < 0.01, we reject Ho.

Hence, there is significant evidence at 0.01 level that the population means in years of spreadsheet usage of students at Montgomery campus is longer than Troy campus. [CONCLUSION]

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Hi! If you use another method/formula in calculating the degrees of freedom in this t-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!

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