9.14 Using JMP

Example 9.14.1 Refer to Example 8.10.1, where we have a data set from a normal population with unknown mean µ and unknown standard deviation s. Test, using JMP, (1) The null hypothesis µ = 30 against (a) µ ? 30 (b) µ > 30, and (c) µ < 30 at the 5% level of significance; (2) The null hypothesis s = 7 against (a) s ? 7 (b) s > 7, and (c) s < 7 at the 5% level of significance.

Solution: To test a hypothesis about the mean µ and the standard deviation s using JMP, proceed as follows:

1. In New Data Table enter the data in Column 1 and label it “Data”.
2. Select from the bar menu Analyze > Distribution. In the new dialog box that appears, select the sample as Y variable. Then click OK.
3. A dialog giving some general results about the distribution appears. From this dialog select the red triangle next to the data name. From the pull-down menu (shown in Figure 8.10.1) select Test Mean. Another dialog box appears where we indicate the hypothesized value, say 30 in this example. Also, if the population standard deviation is known and/or the sample size is large so that we can use the z-test instead of the t-test, then enter the true value or the estimated value of the population standard deviation in the box next to the hypothesized value location.

   The test results in Table 9.14.1 appear. Note that these test results give the p-value for all three alternative hypotheses. All three p-values are greater than the level of significance, 5%. Hence we will not reject the null hypothesis in any case. The diagram in Table 9.14.1 is the distribution of under the null hypothesis.