The z-Test What is the Purpose of a z-Test? What are the Assumptions for a z- Test? How Does a z-Test Work?

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Presentation transcript:

The z-Test What is the Purpose of a z-Test? What are the Assumptions for a z- Test? How Does a z-Test Work?

What is the Purpose of a z-Test? Compare a sample mean to a hypothesized population mean. Test the Null Hypothesis that the sample came from a population with a particular mean. Use for a one-sample design.

What are the Assumptions for a z- Test? Independent observations Interval or ratio level data Normal population or large N (at least 30) Population  is known

How Does a z-Test Work? The sampling distribution is made up of the sample means you would get if the Ho is true. Determine the relative location of the sample mean in the sampling distribution by converting the sample mean to a z- score. Use the normal curve to determine how extreme the sample mean is.

How Does a z-Test Work? If your sample mean is fairly typical (in the middle) for a population where the Ho is true, then fail to reject Ho. If your sample mean is very unusual (on the tail of the distribution) for a population where the Ho is true, then reject Ho.

unusual typical unusual typical