STAT 111 Lecture Notes - Lecture 17: Confidence Interval, Standardized Test, 2Degrees

• School: University of Vermont
• Department: Statistics
• Course: STAT 111
• Professor: Jacob William Martin

Document Summary

Se = the larger the sample size, the smaller the se. If either: a) the variable has a normal distribution in the population (for any sample size, b) or the sample size is at least 30 (for any underlying distribution) x ~ n ( , Usuall(cid:455), (cid:449)e do(cid:374)"t k(cid:374)o(cid:449) the populatio(cid:374) sta(cid:374)dard de(cid:448)iatio(cid:374) ( ), so estimate it with the sample standard deviation, (s) Therefore, we need a distribution that reflects the increased uncertainty. If the populatio(cid:374) is appro(cid:454)i(cid:373)atel(cid:455) (cid:374)or(cid:373)al or the (cid:374) is large (cid:894)(cid:374) (cid:1007)(cid:1004)(cid:895), the(cid:374) a co(cid:374)fide(cid:374)ce interval for can be computed by. Confidence interval for x x t* x (cid:3046) . Degrees of freedom for the t-distribution is n - 1. As degrees get bigger, s gets more accurate. Larger sample size larger degrees t distribution gets closer to normal. T-test for a single mean (cid:3046)(cid:3047)(cid:3047)(cid:3046)(cid:3047) (cid:3048) t = (cid:1867) .