**Hypothesis
Test of Mean, Population Standard Deviation Unknown **

**Brief Description**

Press
*STAT*, choose *TESTS*, choose *T-Test... *and
press *ENTER*. Next to *Inpt**:* choose *Stats* and press *ENTER*.
Enter the correct numbers next to the corresponding symbols. *C-Level* is short for *Confidence Level* and *m** _{0}* is the value of the mean in the
hypotheses. Next to

**Detailed Description**

For demonstration purposes, we will test whether a population mean is at most 41 with 90% confidence given a sample mean of 43.7, a sample standard deviation of 6.2, and a sample size of 25.

Press
*STAT*, choose *TESTS* and then choose *T-Test.../i>
and press ENTER. You will see the
T-Test input screen.*

Next
to *Inpt**:* choose *Stats* by putting the cursor on *Stats*
and pressing the *ENTER* button. Then
enter the correct numbers next to the corresponding symbols. To enter a number,
move the cursor to the right of the symbol using the arrow buttons and press
the buttons for the corresponding digits, adding decimal points and minus signs
if necessary. *C-Level* is short for *Confidence Level* and *m** _{0}* is the value of the mean in the
hypotheses.

When
you have finished, you should have the following on your calculator screen.

_{}

Next to *m**:* you would highlight the option *>**m** _{0}* , since this is the alternative
hypothesis to

_{}

The most important
values given here are the test statistic, t ≈ 2.18, and the P-value, p ≈
0.0198. Even though the calculator gives ten significant digits for each of
these, three significant digits is usually enough. Use enough digits of the
P-value to decide whether it is bigger or smaller than the significance level.
In this case, the P-value is less than the significance level, 1 - 0.90 = 0.10,
so we would reject the null hypothesis. With 90% confidence, there is enough
evidence to say the mean is more than 41.

If
you select *Draw* instead of *Calculate*, the calculator will draw a
normal curve and shade in the area representing the P-value. The drawing
process takes a little longer, but the test statistic and P-value are still
shown at the bottom of the screen. If the P-value is zero in the *Draw* result, go back to *T-Test* and choose *Calculate* instead to see what the P-value is in scientific
notation.