### 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 : **µ**1 – **µ**2 = 0**

** Ha : **µ**1 – **µ**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 = 10**^{2} Ö** 8**^{2} = 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.