Unit3: Statistical Inferences Hypothesis Testing

Unit3: Statistical Inferences

Wenyaw ChanDivision of BiostatisticsSchool of Public HealthUniversity of Texas- Health Science Center at Houston

EstimationPoint EstimatesA point estimate of a parameter is a single number used as an estimate of the value of .e.g. A natural estimate to use for estimating the population mean is the sample mean .Interval EstimationIf an random interval I=(L,U) satisfying Pr(L< 0 When unknown and population is normal

Test Statistic:

Rejection Region: t > tn-1, p-value = 1- Ft,n-1 (t), where Ft,n-1 ( ) is the cdf for t distribution with df=n-1.Note: If is known, the s in test statistic will be replaced by and tn-1, in rejection region will be replaced by z , Ft,n-1 (t) will be replace by (t).

Testing For Two-Sided AlternativeLet X1,.,Xn be the random samples from the population N(, ), where is unknown.H0 : =0 vs H1 : 0 Test Statistic: Rejection Region: |t|> tn-1,1-/2 p-value = 2*Ft,n-1 (t), if t 0. Warning: exact p-value requires use of computer.

Testing For Two-Sided AlternativeP-value for X>U0

P-value for X