Sunday, February 24, 2008

Lecture 7 - Using Minitab to Calculate Hypothesis Testing Statistics

Using Minitab to Calculate Hypothesis Testing Statistics
Minitab can be used to perform some of the calculations that are required in steps 4 and 5 of the critical value approach and step 4 of the p-value approach to hypothesis testing (see previous 2 posts). You still need to do all the study design in steps 1-3 and use them as input to Minitab. You will also need to draw your own conclusions from the calculations that Minitab performs.

Here's how:
1. Load up your data in a Minitab worksheet. (In lecture 7, we used the data in the insurance.mtw worksheet from exercise 9.59.)
2. Select Stat - Basic Statistics from the menu bar. Since we're doing hypothesis testing of the mean, we have 2 choices from the menu. Either "1-sample z" or "1-sample t". Since we don't know the standard deviation of the population, we choose the "1-sample t" test.
3. In the dialog box, select the column that has your sample data and click the select button so it appears in the "Samples in columns" box. In the test mean box, enter the historical value for the mean, which in our case is 45.
4. Click the Options button and enter the confidence level ((1-&alpha)x100) and select a testing "alternative". The testing alternative is where you specify the testing condition of the alternative hypothesis.

  • If H1 states that the mean is not equal to the historical value, select not equal. Minitab will make calculations for a two-tail test.
  • If H1 states that the mean is strictly less than or strictly greater than the historical value, select less than or greater than. In this case, Minitab will calculate values for a one-tail test.
5. Click Ok in the Options dialog and Ok in the main dialog. Minitab displays the calculated values in the Session window. The results from our sample data looked like this:

One-Sample T: Time
Test of mu = 45 vs not = 45

Variable N  Mean    StDev  SE Mean       95% CI        T    P
Time     27 43.8889 25.2835 4.8658 (33.8871, 53.8907) -0.23 0.821

Unfortunately, Minitab doesn't take the hypothesis testing all the way to drawing a conclusion about the null hypothesis. We need to do that ourselves in one of two ways: either the critical value or p-value approach.

For the critical value approach, we need to additionally look up the t-score for t0.025,26 = ±2.056. 0.025 is α/2, which we use with this two-tail test. 26 is n-1, the degrees of freedom for this test. We compare t0.025,26 to the t-score of the sample mean, which Minitab calculated for us as -0.23, and find that the t-score of the sample mean is between the critical values and therefore we do not reject H0.

For the p-value approach, we compare the p-value that Minitab calculated as 0.821 and compare that to the level of significance, &alpha, which in our case is 0.10. Since the p-value is larger than α we do not reject H0.

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