ECON10005 Lecture Notes - Lecture 6: Sampling Distribution, Central Limit Theorem, Bias Of An Estimator
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Mean of the sampling distribution is the (cid:374)u(cid:373)(cid:271)er of (cid:862))u(cid:272)ker(cid:271)erg(cid:863) respo(cid:374)ses is the sa(cid:373)ple proportio(cid:374) (cid:894)sa(cid:373)ple (cid:373)ea(cid:374)(cid:895) of (cid:862))u(cid:272)ker(cid:271)erg(cid:863) Week (cid:1010) lecture (cid:1005: define, 1, if response is (cid:862))u(cid:272)ker(cid:271)erg(cid:863, 0, if response is (cid:862)thelo(cid:374)ious(cid:863, then (cid:3041)=(cid:2869, =(cid:2869)(cid:3041) (cid:3041)=(cid:2868, consider what different values of might result from taking different sample of size 10. Or further away: would increasing produce a better in some sense, denote mean of the random variables as (cid:4666)(cid:4667), the mean of the random variable is therefore (cid:4666) (cid:4667)=((cid:883) . Variance of the sampling distribution: the variance (or s. d. ) of the sampling distribution measures the dispersion around the mean of the possible values for the estimates. Larger samples only improve the variance of the sample mean: a(cid:374) esti(cid:373)ator (cid:449)ith a s(cid:373)aller (cid:448)aria(cid:374)(cid:272)e is (cid:373)ore (cid:862)pre(cid:272)ise(cid:863, suppose (cid:2869),(cid:2870), are independent and (cid:1853)(cid:4666)(cid:4667)=(cid:2870) (cid:1853)(cid:4666) (cid:4667)=(cid:1853)((cid:883) . If (cid:2869),(cid:2870), are independent and (cid:1853)(cid:4666)(cid:4667)=(cid:2870) then (cid:1853)(cid:4666) (cid:4667)=2(cid:3041: larger is more precise, larger (cid:2870) is less precise, is said to be consistent because.
