Question

Students enrolled in an introductory statistics course at a university were asked to take a survey that indicated whether the student’s learning style was more visual or verbal. Each student received a numerical score ranging from -11 to +11. Negative scores indicated a visual learner, and positive scores indicated a verbal learner. The closer the score was to -11 or +11, the stronger the student’s inclination toward that learning style. A score of 0 would indicate neutrality between visual or verbal learning.  For the 39 students who took the survey, the mean score was -2.744, and the standard deviation was 4.988.

A. State the null and alternative hypotheses for testing whether the mean score (among all students at this university) differs from 0.

B. Calculate the value of the t-test statistic for the hypotheses stated in question 1.

C. Determine the p-value of the test as accurately as possible.

D. Summarize the conclusion that you would draw from this test.

E. Comment on whether the technical conditions of this t-test are satisfied.

Answer 1

a)

Ho :   µ =   0                  
Ha :   µ ╪   0       (Two tail test)          
                          
Level of Significance ,    α =    0.05                  
sample std dev ,    s =    4.9880                  
Sample Size ,   n =    39                  
Sample Mean,    x̅ =   -2.7440                  
                          
degree of freedom=   DF=n-1=   38                  
                          
Standard Error , SE = s/√n =   4.9880   / √    39   =   0.7987      

b)

t-test statistic= (x̅ - µ )/SE = (   -2.744   -   0   ) /    0.7987   =   -3.436

..........

c)   
                          
p-Value   =   0.0014   [Excel formula =t.dist(t-stat,df) ]              

d)

Decision:   p-value<α, Reject null hypothesis                       

the mean score (among all students at this university) differs from 0.

/......................

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