**Hypothesis
Test of Mean - Population Standard Deviation Known
**

**Brief Description**

Press
*STAT*, choose *TESTS*, choose *Z-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 hypothesis. Next to *m**:* choose the option representing the
correct alternative hypothesis and press *ENTER*.
Finally, choose *CALCULATE* in the last
line and press *ENTER*. The test
statistic is next to *z =* and the
P-value is next to *p =*.

**Detailed Description**

To demonstrate this procedure we will use a sample mean of 58.1, a population standard deviation of 2.3, a sample size of 40, and suppose we want to test whether the mean is at least 58.5 with 95% confidence.

Press
*STAT*, choose *TESTS* and then choose *Z-Test...*
and press *ENTER*. You will see the Z-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
hypothesis.

When
you have finished, the numbers should appear as shown below.

_{}

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

_{}

The most important values given here are the test statistic, z ≈ -1.10, and the P-value, p ≈ 0.136. 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 greater than the significance level, 1 - 0.95 = 0.05, so we would keep the null hypothesis.With 95% confidence, there is not enough evidence to say the mean is less than 58.5.

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.