ECON10005 Lecture Notes - Lecture 7: Test Statistic, Type I And Type Ii Errors, Bias Of An Estimator
Document Summary
Variance estimation: the sample variance can be shown to be an unbiased estimator of population variance (cid:4666)(cid:1871)(cid:2870)(cid:4667)=(cid:2870) It can be shown the clt continues to work: (cid:1871) (cid:1866) ~(cid:4666)(cid:882),(cid:883)(cid:4667) (cid:1870)(cid:4666)(cid:1872)(cid:4667)=(cid:1866) (cid:883) (cid:1866) 3 (cid:1858)(cid:1867)(cid:1870) (cid:1866)>3. If is normally distributed then \ (cid:3041)~(cid:1872)(cid:3041) (cid:2869) exactly: although can never be exactly normally distributed, the t distribution is very similar to the normal distribution, the t distribution has a (slightly) larger variance than the normal: It depends on the degrees of freedom, which is n-1 t-distribution: as n increases, the t and the normal distribution become more and more indistinguishable. Week (cid:1011) lecture (cid:1006: rejecting (cid:2868) when it is true. Decisions in hypothesis testing: possible outcomes for a two tail test: Reject (cid:2868: the probability of making at type i error is just the significance level. Value of in the population: rejecting (cid:2868) when it is true.
