STA 2023H Lecture Notes - Lecture 25: Confidence Interval, Central Limit Theorem, Sampling Distribution
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Shape of sa(cid:373)pli(cid:374)g dist(cid:396)i(cid:271)utio(cid:374) is depe(cid:374)de(cid:374)t o(cid:374) the populatio(cid:374) that"s sa(cid:373)pled. Solutio(cid:374): use the stude(cid:374)t"s t statisti(cid:272) if, a(cid:374)d o(cid:374)ly if, the p(cid:396)o(cid:271)le(cid:373) is normal. Solution: use the student t distribution (pink sheet tables) instead of z distribution. Student t distribution: t = ([sample mean] [mean])/(s/[square root of n] There are many t distributions to choose from depending on your degrees of freedom (df = n-1) As n approaches infinity, t approaches z. Deg(cid:396)ees of f(cid:396)eedo(cid:373) (cid:894)df(cid:895): if (cid:1007) test s(cid:272)o(cid:396)es have a (cid:373)ea(cid:374) of (cid:1012)(cid:1004), (cid:1006) (cid:272)a(cid:374) (cid:271)e (cid:862)f(cid:396)ee(cid:863); (cid:271)ut, the (cid:1007)rd must be: (80x3) the other 2. If n is greater than or equal to 30, use the. Sample mean ta/2 s/[s(cid:395)ua(cid:396)e (cid:396)oot of (cid:374)] To find ta/2, look at 95% confidence interval and degrees of freedom on pink sheet tables. (cid:1013)(cid:1004)(cid:1004) (cid:1006). (cid:1005)(cid:1007)(cid:1005) (cid:1005)(cid:1006)(cid:1004)/[s(cid:395)ua(cid:396)e (cid:396)oot of (cid:1005)6]
