Example of a 1-Sample t-Test and t-Confidence Intervalmain topic interpreting results session command see also
Example of a 1-Sample t-Test and t-Confidence IntervalMeasurements were made on nine widgets. You know that the distribution of widget measurements has historically been close to normal, but suppose that you do not know s. To test if the population mean is 5 and to obtain a 90% confidence interval for the mean, you use a t-procedure.
1 Open the worksheet EXH_STAT.MTW.
2 Choose Stat > Basic Statistics > 1-Sample t.
3 In One or more samples, each in a column, enter Values.
4 Check Perform hypothesis test. In Hypothesized mean, enter 5.
5 Click Options. In Confidence level, enter 90. Click OK in each dialog box.
Session window output
One-Sample T: Values
Test of μ = 5 vs ≠ 5
Variable N Mean StDev SE Mean 90% CI T P Values 9 4.7889 0.2472 0.0824 (4.6357, 4.9421) -2.56 0.034 |
The test statistic, T, for H0: m = 5 is calculated as -2.56.
The p-value of this test, or the probability of obtaining more extreme value of the test statistic by chance if the null hypothesis was true, is 0.034. This is called the attained significance level, or p-value. Therefore, reject H0 if your acceptable a level is greater than the p-value, or 0.034.
A 90% confidence interval for the population mean, m, is (4.6357,4.9421). This interval is slightly wider than the corresponding Z-interval shown in Example of 1-Sample Z.