A company that makes language learning software wants to det

A company that makes language learning software wants to determine which of two approaches (Method A or Method B) to learning vocabulary would lead to the largest number of recalled words. The company wishes to evaluate the methods on 7 different languages (since languages differ in difficulty). Seven individuals, one per language, were recruited to learn words using Method A, and 7 individuals, one per language, were recruited to learn words using Method B.  The data, representing the number of words recalled, is shown below.

The company wishes to test whether there is a difference in the average number of words recalled using the two methods. Calculate the test statistic for this hypothesis to two decimal places. Hint: This is a matched pairs design.

Solution

Let ud = u2 - u1.              
Formulating the null and alternative hypotheses,              
              
Ho:   ud   =   0  
Ha:   ud   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
              
Calculating the standard deviation of the differences (third column):              
              
s =    6.141636343          
              
Thus, the standard error of the difference is sD = s/sqrt(n):              
              
sD =    2.321320344          
              
Calculating the mean of the differences (third column):              
              
XD =    -1          
              
As t = [XD - uD]/sD, where uD = the hypothesized difference =    0   , then      
              
t =    -0.430789315 = -0.43 [ANSWER]