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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 m0 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 m0 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 < m0, since that is the alternative hypothesis to μμ0 where μ0 = 58.5. 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 ≈ -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.

 

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