Because most samples have x’s that are close to μ, most will have t-scores that are close to zero. When you look at the formula for the t-score, you should be able to see that the mean t-score is zero because the mean of the x’s is equal to μ. As introduced in Chapter 2, Figure 5.1 reproduces a portion of a typical t-table within an interactive Excel template.įigure 5.1 Interactive Excel Template for Determining Cut-off Point of a t-Table – see Appendix 5. Luckily, you do not have to generate your own t-distributions because any statistics book has a table that shows the shape of the t-distribution for many different degrees of freedom. When you have all of the samples’ t-scores, form a relative frequency distribution and you will have your t-distribution. You could generate your own t-distribution with n-1 degrees of freedom by starting with a normal population, choosing all possible samples of one size, n, computing a t-score for each sample, where: The t-distribution is a sampling distribution. Before we start to learn about those tests, a quick review of the t-distribution is in order. You will also have a chance to use the interactive Excel templates to apply the t-test in alternative situations. You will learn how to use the t-test in three different types of hypotheses. Here you will learn how to use that same t-distribution to make more inferences, this time in the form of hypothesis tests. In Chapter 4, you learned how to use the t-distribution to make an important inference, an interval estimate of the population mean. In Chapter 3, a sampling distribution, the t-distribution, was introduced.
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