Hypothesis for Small Samples

• When we have a small sample from a normal population, we use the same method as a large sample except we use the t-statistic instead of z-statistic. Hence, we need to find the degrees of freedom (n-1) and use the t-table in the back of the book.
• A z-statistic is usually used for large sample size (n greater or equal to 30) drawn randomly. The population standard deviation is estimated by the sample standard deviation. The t curves are bell shaped and distributed arond t=0. The exact shape on a given t-curve depends on the degree of freedom. In case of performing multiple comparisions by on way Anova, the F-statistic is normally used. The critical value of 'F' is read off from the tables on the F-distrubition knowing the type I error and the degree of freedom betwen and within the groups.