HSS 2381 Lecture Notes - Lecture 6: Normal Distribution, Central Limit Theorem, Point Estimation
17 Oct 2017
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Tables at the end (z and t table). The sampling distribution of this statistic is the standard normal distribution. The replacement of sigma by s leaves this distribution unchanged only if the sample size n is large. The sampling distribution of: (we use this type of statistic when we don"t have a large enough sample) is called students t distribution with n 1 degrees of freedom. In the previous lectures (estimation, hypothesis testing), we used the z statistic even when we did not know . In that case, we used s as a point estimate of for large enough n. William s. gossett, who developed the t-distribution, wrote under the name student since, as an employee of the. Guinness brewery in dublin, he was required by the firm to use a pseudonym in publishing his results. We use the t-distribution when we have small samples.
