### 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 : µ1 – µ2 = 0

Ha : µ1 – µ2 ­ 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 Ö 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.