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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. p0 denotes the population proportion, x denotes the number of successes, and n denotes the sample size.

Next to prop highlight ≠p0 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. p0 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 ≠p0, since this is the alternative hypothesis to prop = p0 where p0 = 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.

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