Single-Sample t-Test What is the Purpose of a Single-Sample t- Test? How is it Different from a z-Test?What Are the Assumptions?

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Single-Sample t-Test What is the Purpose of a Single-Sample t- Test? How is it Different from a z-Test?What Are the Assumptions?

What is the Purpose of a Single- Sample t-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.

How is it Different from a z-Test? The z test requires you to know the , but you usually don’t know it. If you don’t know , your best estimate of it is s x. When you use s x instead of , you are doing a t-test.

Comparing z and t

How is it Different? The t distribution is symmetrical but flatter than a normal distribution. The exact shape of a t distribution depends on degrees of freedom

normal distribution t distribution

What Are Degrees of Freedom? Amount of information in the sample Changes depending on the design and statistic For a one-group design, df = N-1 The last score is not “free to vary”

What are the Assumptions? Independent observations. Interval or ratio level data. Population distribution is symmetrical.