# Discussion08.pdf - Stat 324 Discussion 08 One Population...

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Stat 324Discussion 08One Population Tests SummaryBelow we consider only the situation whenσ2is unknown, since in practical situations the population varianceσ2is generally unknown.1. When the data is normal andσ2is unknown, use a t-test (One sample t-test)To test:1H0:μ=μ0HA:μ6=μ0,2H0:μ=μ0HA:μ > μ0,or3H0:μ=μ0HA:μ < μ0at the significance levelαbased on a sample of sizen, use one of the following methods:Then computeTobs=¯x-μ0s/nand reject the null if1tobs<-t(n-1,α/2)ortobs> t(n-1,α/2),2tobs> t(n-1),or3tobs<-t(n-1).whereP(tn-1t(n-1)) =α.Using the p-value method, compute1p-value=P(t(n-1)≤ -|tobs|) +P(t(n-1)≥ |tobs|) = 2P(t(n-1)≥ |tobs|),2p-value=P(t(n-1)tobs),or3p-value=P(t(n-1)tobs).RejectH0if p-value< α. Else fail to rejectH0.Using the CI method (only for the two-sided test), find at-based 100(1-α)% CI forμ. Ifμ0is in theinterval, we fail reject the null. Ifμ0is not in the interval, we reject the null.2. When the data is not normal butnis large enough that the CLT applies (typicallyn30), use a z-test(One sample z-test)To test:1H0:μ=μ0HA:μ6=μ0,2H0:μ=μ0HA:μ > μ0,or3H0:μ=μ0HA:μ < μ0at the significance levelαbased on a sample of sizen, use one of the following methods:
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