A new prep class was designed to improve SAT math test score

A new prep class was designed to improve SAT math test scores. Five students were selected at random. Their scores on two practice exams were recorded; one before the class and one after. The data recorded in the table below. We want to test if the scores, on average, are higher after the class.

SAT Math Score

Student 1

Student 2

Student 3

Student 4

Student 5

Score before the class

620

700

650

640

620

Score after the class

640

700

670

670

630

What is the test statistic? (Show work and round the answer to three decimal places)

Solution

Consider the table:

  
              
Calculating the standard deviation of the differences (third column):              
              
s =    10.7308674          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    4.798989793          
              
Calculating the mean of the differences (third column):              
              
XD =    16          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    3.334035014 = 3.334 [ANSWER]