Again, we assume that the (theoretical) population mean is 4, the sample mean is 5.0, and the sample standard deviation s is 1.936. Now, the standard error will be When N = 20, the critical value for a 5% significance test will be 2.09 (because the t-distribution curve is closer to the normal distribution). Why the t-distribution is a family of curves. 2  How critical t-values change as a function of the alternative hypothesis and the Type I error rate. 3  How to calculate t-values for a single sample t-test, an independent samples t-test, and a paired t-test.
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