Two Sample T-Test


Sample of Final Exam scores from two statistics classes with different instructors provided the following results:

     Instructor A           Instructor B

        n1 = 12                n2 = 15

        x1 = 72                 x2 = 79

        s1 = 8                   s2 = 10

Using a = .05, test whether these data are sufficient to conclude that the population mean grades differ for the two instructors.

First we need to develop the null and alternative hypothesis.

Ho : 1 – 2 = 0

Ha : 1 – 2 0 and we will reject Ho if p < .05

For this problem we will use a T-test. Start from the “TESTS” menu.

Press Arrow right to "TESTS" and Arrow down to "4 : 2-SampTTest..."

Press (see screen below )

 

Choose "Stats" and press

Next, match the settings on your calculator to those on the above screen.

Be sure you highlight the alternative test "".

Now we need to calculate the F Test statistic.

F = 102 82 = 100 / 64 = 1.5625

Again we can assume equal variances so highlight "Yes".

Arrow down to "Calculate" and press (see screen below)



 


As you can see from the screen above the p-value = .06 which is not less than .05 therefore we can not reject Ho .

In conclusion we must say that at the alpha = .05 level there is not sufficient evidence to claim that the mean test scores between the two instructors differ.