MAST10011 Chapter Notes - Chapter 6: Sample Size Determination, Null Hypothesis, Statistical Hypothesis Testing

• School: University of Melbourne
• Department: Mathematics and Statistics
• Course: MAST10011
• Professor: Dr Rheanna Mainzer

Document Summary

Type i error: reject null hypothesis when the null hypothesis is true (probability = , signifi(cid:272)ant le(cid:448)el = ) Type ii error: don"t reje(cid:272)t null hypothesis (cid:449)hen the alternati(cid:448)e is true (pro(cid:271)a(cid:271)ility = , po(cid:449)er = 1 - ) , reject the null if z < -1. 96 or z > 1. 96 (at a 0. 05 significance level) 3 methods: confidence interval: as above p-value: if the null hypothesis is true, p is the probability of observing a certain value as far away from the mean as the one observed. Reject the null if p<0. 05 and say the result is stastically significant. Sample size determination: critical values: z-test: z=x 0 n t-test testing = when is unknown: use for a small n. , observed = 0 when the null is true, then = (cid:2869) Approximate z-test testing = when is unknown: use for large n. (cid:2868)(cid:4666)(cid:883) (cid:2868)(cid:4667) when the null is true, then (cid:4666)(cid:882),(cid:883)(cid:4667) provided n is large.