Question

In: Statistics and Probability

The administration at a university is interested in studying if any relationship exists between quality of...

The administration at a university is interested in studying if any relationship exists between quality of academic experience at the school and whether the student is a major in the College of Humanities and Social Sciences (HSS major) or has a major in the College of Business (Business major). The school randomly surveys 10 seniors who are HSS students and 10 seniors who are Business students and asks them to rate the quality of their academic experience on a scale of 1-10, where 10 is extremely high and 1 is extremely low. Here are the data:

HSS Major Business Major
7 4
6 7
10 4
4 6
8 8
9 7
6 9
8 5
7 8
10 7

The HSS majors have a mean of 7.5 and a variance of 3.6, whereas the Business majors have a mean of 6.5 and a variance of 2.9.

Answer the following questions:

1. What is the null hypothesis? (1 point)

2. What is the research hypothesis? (1 point)

3. What is the dependent variable? (1 point)

4. Write out the results of an independent samples t-test using these data. In other words, provide the numerical answers: t-statistic, your critical value of t (or p-value), and degrees of freedom. (4 points)

5. Write a paragraph to explain the results of the hypothesis test using statistics from the problem with alpha=0.05. This should be two or more formal sentences to describe your findings and conclusions.

Solutions

Expert Solution

1)

Ho :   µ1 - µ2 =   0  

Mean difference in score of quality between College of Humanities and Social Sciences (HSS major) and   major in the College of Business (Business major) is zero

2)

  
Ha :   µ1-µ2 ╪   0  
   

Mean difference in score of quality between College of Humanities and Social Sciences (HSS major) and   major in the College of Business (Business major) is not zero.

3)

Dependent variable: mean difference

4)


                          
Level of Significance ,    α =    0.05                  
                          
Sample #1   ---->   sample 1                  
mean of sample 1,    x̅1=   7.50                  
standard deviation of sample 1,   s1 =    1.90                  
size of sample 1,    n1=   10                  
                          
Sample #2   ---->   sample 2                  
mean of sample 2,    x̅2=   6.50                  
standard deviation of sample 2,   s2 =    1.72                  
size of sample 2,    n2=   10                  
                          
difference in sample means =    x̅1-x̅2 =    7.5000   -   6.5   =   1.00  
                          
pooled std dev , Sp=   √([(n1 - 1)s1² + (n2 - 1)s2²]/(n1+n2-2)) =    1.8105                  
std error , SE =    Sp*√(1/n1+1/n2) =    0.8097                  
                          
t-statistic = ((x̅1-x̅2)-µd)/SE = (   1.0000   -   0   ) /    0.81   =   1.235
                          
Degree of freedom, DF=   n1+n2-2 =    18                  
t-critical value , t* =        2.1009   (excel formula =t.inv(α/2,df)              
Decision:   | t-stat | < | critical value |, so, Do not Reject Ho                      
p-value =        0.232680   (excel function: =T.DIST.2T(t stat,df) )      

5)
Conclusion:     p-value>α , Do not reject null hypothesis              

Mean difference in score of quality between College of Humanities and Social Sciences (HSS major) and   major in the College of Business (Business major) is not different from zero.       


THANKS

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