STAT 1000Q Lecture Notes - Lecture 21: Confidence Interval, Prostate Cancer
23 Oct 2017
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Md= unknown true mean of the population differences. Confidence interval for the mean of differences. Example: before and after sat scores from a prep course. Take their differences t= d(cid:271)a(cid:396)/sd x (cid:374) so (cid:1005)(cid:1012). (cid:1009)(cid:1011)/(cid:1007)(cid:1007). (cid:1006)(cid:1010) x (cid:1011) = (cid:1005). (cid:1008)(cid:1011)(cid:1011) 0. 095>0. 05 so we do not reject the h0. Confidence interval of 95% for previous example. 18. 57 (dbar) +/- (cid:1006). (cid:1008)(cid:1008)(cid:1011) (cid:894)(cid:1007)(cid:1007). (cid:1006)(cid:1010)(cid:895)/ (cid:1011) = (cid:1005)(cid:1012). (cid:1009)(cid:1011) +/- 30. 76. It straddles 0, so insufficient evidence that the prep course works. N1xp1 and n2xp2 all have to be greater than or equal to 15 to be normal. P1-p2 +/- ) (cid:894)i(cid:374)v(cid:374)o(cid:396)(cid:373)(cid:895) x (cid:894)(cid:894)p(cid:1005) x (cid:395)(cid:1005)/(cid:374)(cid:1005)(cid:895) + (cid:894)p(cid:1006) x (cid:395)(cid:1006)/(cid:374)(cid:1006)(cid:895)(cid:895) Ci= (0. 253-0. 31) +/- i(cid:374)v(cid:374)o(cid:396)(cid:373)(cid:894)(cid:1004). (cid:1013)(cid:1011)(cid:1009)(cid:895) x (cid:894)(cid:894)(cid:1004). (cid:1006)(cid:1009)(cid:1007) x (cid:1004). (cid:1011)(cid:1008)(cid:1011)/(cid:1005)(cid:1009)(cid:1004)(cid:1004)(cid:895) + (cid:894)(cid:1004). (cid:1007)(cid:1005) x. The interval is all in the negatives so we can be 95% confident that n1 is less than n2. Ha: p1-p2 > or < or not equal to 0.
