Six Sigma Green Belt Certification Practice Exam

A sample Z-test for population means concludes that the null hypothesis should not be rejected. This means that statistically the sample mean is ________ the population mean.

1. The same as

2. Different than

3. Larger than

4. Not related

The correct answer is: The same as

The correct answer indicates that statistically, the sample mean is considered to be the same as the population mean in the context of the Z-test. When the conclusion of a Z-test is that the null hypothesis should not be rejected, it implies that there is insufficient evidence to suggest a difference between the sample mean and the population mean. In statistical terms, failing to reject the null hypothesis means that the sample data did not provide strong enough evidence to support a claim that the sample mean is significantly different from the population mean. Therefore, we consider that any observed difference could be attributed to random sampling variability rather than a true difference in the population parameters. The other choices convey notions of difference or unrelatedness between the sample mean and population mean, which contradicts the outcome of a Z-test that does not reject the null hypothesis.