STATS 2B03 Chapter Notes - Chapter 7: Confidence Interval, Statistical Parameter, Standard Deviation

• School: McMaster University
• Department: Statistics
• Course: STATS 2B03
• Professor: Aaron Childs

Document Summary

Example mendel bred green and yellow peas (picture) 428 were green and 152 blue. (cid:2869)(cid:2873)(cid:2870)(cid:2873)(cid:2876)(cid:2868)=(cid:884)(cid:888). (cid:884)% Confidence interval (ci): for a populatio(cid:374) para(cid:373)eter ra(cid:374)ge of (cid:448)alues used to esti(cid:373)ate the para(cid:373)eter (cid:271)ased o(cid:374) a sample. Confidence level: the proportion of times that the confidence interval will actually contain the parameter. Result: p= proportion of peas that should be yellow, p= proportion of people with a certain disease let (cid:1868) denote a sample proportion. A 100(1- (cid:895)% ci for p is (cid:1868) (cid:1831) where (cid:1831)= (cid:3043) (cid:3044) is called the (cid:862)(cid:373)argi(cid:374) of error(cid:863) (cid:894)a(cid:374)d (cid:1869) = (cid:883) (cid:1868) ) (should only be used if n(cid:1868) 5 a(cid:374)d (cid:374)(cid:1869) 5(cid:895) Example find a 95% ci for the true proportion of yellow peas. So n(cid:1868) =(cid:883)(cid:887)(cid:884) and n(cid:1869) =(cid:887)(cid:890)(cid:882)(cid:4672)(cid:883) (cid:2869)(cid:2873)(cid:2870)(cid:2873)(cid:2876)(cid:2868)(cid:4673)=(cid:886)(cid:884)(cid:890) a(cid:374)d (cid:271)oth are 5. Ie. we estimate that 22. 6% < p < 29. 8% If the experiment is repeated a large number of times, then the ci will contain the true proportion.