PSYCH 2220 Lecture Notes - Lecture 9: Square Root, Normal Distribution, Statistical Hypothesis Testing
7 Mar 2018
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Chapter 9 - the single sample t test. Used when the parameters are not known. Estimate a pop. st dev from a sample. Assumes the sample st. dev underestimates the pop. st dev. We sample 5 employees and see scores of 8, 12, 16, 12, and 14 minutes. Mu = 11, n = 5, sample mean, m = (8+12+16+12+14)/5 = 12. 4. Square root of 35. 2 / (5 - 1) = 2. 97 = s. Sm = 2. 97 / (cid:887) = 1. 33 t = (12. 4 - 11) / 1. 33 = 1. 05. The t statistic t = (m - mu) / sm t is the distance of the sample mean from the pop. mean in terms of estimated st error. And t and z distributions become more equal. It"s more likely to reject the null when you shouldn"t (type i error) when your sample is small but you use the z distribution. Z underestimates variance, and would have too many type i errors.
