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Unformatted text preview: Hypothesis Testing Goal: Make statement(s) regarding unknown population parameter values based on sample data Elements of a hypothesis test: Null hypothesis  Statement regarding the value(s) of unknown parameter(s). Typically will imply no association between explanatory and response variables in our applications (will always contain an equality) Alternative hypothesis Statement contradictory to the null hypothesis (will always contain an inequality) Test statistic  Quantity based on sample data and null hypothesis used to test between null and alternative hypotheses Rejection region  Values of the test statistic for which we reject the null in favor of the alternative hypothesis Hypothesis Testing Test Result True State H True H False H True Correct Decision Type I Error H False Type II Error Correct Decision ) ( ) ( Error II Type P Error I Type P = = Goal: Keep , reasonably small Example  Efficacy Test for New drug Drug company has new drug, wishes to compare it with current standard treatment Federal regulators tell company that they must demonstrate that new drug is better than current treatment to receive approval Firm runs clinical trial where some patients receive new drug, and others receive standard treatment Numeric response of therapeutic effect is obtained (higher scores are better). Parameter of interest: New Std Example  Efficacy Test for New drug Null hypothesis  New drug is no better than standard trt ( 29 : =  Std New Std New H Alternative hypothesis  New drug is better than standard trt : Std New A H Experimental (Sample) data: Std New Std New Std New n n s s y y Sampling Distribution of Difference in Means In large samples, the difference in two sample means is approximately normally distributed: + 2 2 2 1 2 1 2 1 2 1 , ~ n n N Y Y Under the null hypothesis, 1 2 =0 and: ) 1 , ( ~ 2 2 2 1 2 1 2 1 N n n Y Y Z + = 1 2 and 2 2 are unknown and estimated by s 1 2 and s 2 2 Example  Efficacy Test for New drug Type I error ...
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This note was uploaded on 07/28/2011 for the course STA 6934 taught by Professor Young during the Fall '08 term at University of Florida.
 Fall '08
 YOUNG

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