1. In the x2 test, why is it that only the area in the upper tail of the χ2 distribution is of interest?
2. Suppose it is known in a large urban school district that four out of five teenagers who join a gang subsequently drop out of high school. A "stay in school" intervention is instituted for a sample of 45 gang members. It is later found that 30 of these students have remained in school and 15 dropped out. Is the intervention effective?
(a) Give H0 and H1 in terms of the proportion of gang members who drop out of high school.
(b) Compute χ2 and perform the test at α = 05.
(c) Draw final conclusions.