Statistical Sciences 2141A/B Lecture Notes - Lecture 28: Test Statistic, Statistical Hypothesis Testing, Weighted Arithmetic Mean

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

Document Summary

Data from two independent samples consists of two independent sets of observations x1, x2, , xm (cid:894)(cid:449)ith (cid:373)ea(cid:374) a a(cid:374)d (cid:448)aria(cid:374)(cid:272)e a: and y1, y2, , yn (cid:449)ith (cid:894)(cid:449)ith (cid:373)ea(cid:374) b a(cid:374)d (cid:448)aria(cid:374)(cid:272)e b. The sample sizes m and n may not be equal, since it may be more difficult or expensive to sample one population than another or because some of the study subjects drop out of the experiment. If (cid:271)oth populatio(cid:374)s are (cid:374)or(cid:373)al populatio(cid:374)s a(cid:374)d the (cid:448)alues of (cid:271)oth a. We can use a z-test to test the following: We (cid:272)a(cid:374) also (cid:272)o(cid:374)stru(cid:272)t (cid:272)o(cid:374)fide(cid:374)(cid:272)e i(cid:374)ter(cid:448)als for a - b. Example 9. 6: c c c v c v c v v c c v c c v . O(cid:374)(cid:272)e agai(cid:374), the issue (cid:449)ith this hypothesis test is that the populatio(cid:374) (cid:448)aria(cid:374)(cid:272)es a usually unknown. One approximation is to substitute the sample standard deviations sa and sb for a a(cid:374)d b in the calculation of the test statistic.