Statistical Sciences 2141A/B Lecture 24: Section 8.1

• School: Western University
• Department: Statistical Sciences
• Course: Statistical Sciences 2141A/B
• Professor: Joe Raaymakers

Document Summary

A point estimate, because it is a single number, provides no information about the precision and reliability of estimation. An alternative to calculating a single sensible value is to calculate an entire interval of plausible values a confidence interval. A confidence interval includes a measure of the degree of reliability of the interval a confidence level. Recall that if x1 , x2 n " n(cid:894) , 2) distribution. From the z (standard normal) table we know that. The interval is referred to as a confidence interval (ci) and the probability (95%) is the confidence level. Other typical confidence levels are 90% and 99% A 100(1 (cid:895)% (cid:894)t(cid:449)o-sided(cid:895) (cid:272)o(cid:374)fide(cid:374)(cid:272)e i(cid:374)ter(cid:448)al (cid:894)ci(cid:895) for the (cid:373)ea(cid:374) of a (cid:374)or(cid:373)al populatio(cid:374) (cid:449)he(cid:374) the (cid:448)alue of is k(cid:374)o(cid:449)(cid:374) is gi(cid:448)e(cid:374) (cid:271)(cid:455) (cid:449)here z /2 is a (cid:272)riti(cid:272)al (cid:448)alue fro(cid:373) the sta(cid:374)dard (cid:374)or(cid:373)al. T + (z critical value) * (standard error of mean) Note that as n increases, the interval narrows.