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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 m0 is the value of the mean in the hypotheses. 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 t = and the P-value is next to p =.

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 m0 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 >m0 , since this is the alternative hypothesis to μμ0 where μ0 = 41. 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, 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.

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