Data Analysis CourseTests of Location for a Single Population - SummaryDraft: January 13, 2016Tests of Location for a Single Population1. When the data is drawn from a population that has a normal distribution andσis unknown, use a t-test.To test:H0:μ=μ0HA:μ6=μ0at the 100α% level based on a sample of sizen, use one of the following methods:•Using the rejection region method, determine the valuet(n-1,α/2)so that:P(-t(n-1,α/2)≤t≤t(n-1,α/2)) = 1-α.Then computetobs=¯x-μ0s√n. Reject the null iftobs<-t(n-1,α/2)ortobs> t(n-1,α/2).•Using the p-value method, computep-value=P(t(n-1)<-|tobs|) +P(t(n-1)>|tobs|).Reject ifp-value < α.•Using the CI method, find at-based 100(1-α)% CI forμ. Ifμ0is in the interval, do not reject thenull. If it is not in the interval, reject the null.2. When the data is drawn from a population that has a normal distribution andσis known, the sample sizenrequired to achieve power 1-βfor a test ofH0:μ=μ0vs.HA:μ6=μ0when the realμisμAat levelαis approximately:n= (σ(zα/2+zβ)μ0-μA)2.