Question

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.

After one month, each person completed a test of word recall. The data, representing the number of words recalled, are shown in the table below.

Method A	Method B
13	30
10	36
8	19
3	36
22	31
8	8
22	37

The company wishes to test whether there is a difference in the average number of words recalled between the two methods. Calculate the test statistic for this hypothesis to two decimal places. Take all calculations toward the final answer to three (3) decimal places.

Answer 1

H0: mu(A) = mu(B)
Ha: mu(A) not equals to mu(B)

xbar(A) = 12.2857  
xbar(B) = 28.1429
s(A) = 7.2736
s(B) = 10.8233

SE = sqrt(7.2736^2/7 + 10.8233^2/7) = 4.9288

Test statistic,
t = (12.2857 - 28.1429)/4.9288
t = -3.2173

df = 11
p-value = 0.0082

As p-value < 0.05, reejct H0
There are significant evidence to conclude that the mean of the two methods are different