**Hypothesis
Test of Proportion**

**Brief Instructions**

Press
*STAT*, choose *TESTS*, choose *1-PropZTest...*
and press *ENTER*. Enter the correct
numbers next to the corresponding symbols. *p**0* denotes the population proportion,
x denotes the number of successes, and *n*
denotes the sample size.

Next
to prop highlight ≠*p**0*
and press *ENTER*. Then choose *Calculate* and press *ENTER*. The test statistic is next to *t* = and the P-value is next to *p* =.

**Detailed Instructions**

To demonstrate this procedure suppose we have 34 successes in a sample of size 80, and want to test whether the proportion is 0.40 with 90% confidence.

Press
*STAT*, choose *TESTS* and then choose *1-PropZTest...*
and press *ENTER*. You will see the *1-PropZTest* input screen.

Enter
the correct numbers next to the corresponding symbols. *p**0* denotes the population proportion,
*x* denotes the number of successes,
and *n* denotes the sample size. 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 if necessary.

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

_{}

Next to *prop* you would highlight the option ≠*p**0*, since this is the alternative
hypothesis to *prop* = *p**0* where *p**0* = 0.4. Then press *ENTER* to make sure this option is
selected. Finally, put the cursor on *Calculate*
and press *ENTER*. You should see the
following results.

_{}

The most important values given here are the test statistic, z ≈ 0.456, and the P-value, p ≈ 0.648. Even though the calculator gives nine and ten significant digits for these values, three significant digits are usually sufficient. 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 more than the significance level, 1 - 0.98 = 0.02, so we would keep the null hypothesis. With 98% confidence, there is not enough evidence to say the proportion is not 0.40.

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 shown as 0 or 1 when *Draw* is selected, you return to the
1-PropZTest... screen and choose *Calculate*
instead. The P-value given by calculate is usually a number in scientific
notation, and not 0 or 1.