Hypothesis Tests for Proportions. The Random Variable Recall –Normal distribution –Mean  = p –Standard Deviation =

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Presentation transcript:

Hypothesis Tests for Proportions

The Random Variable Recall –Normal distribution –Mean  = p –Standard Deviation =

Hypothesis Testing for Proportions H 0 : p = p 0 H A : p > p 0 Test is Reject H 0 (Accept H A ) if z > z  The test statistic, z, is:

EXAMPLE Taste test between Coke and Pepsi 1000 cola drinkers tested 540 say they prefer Coke Can we conclude that more than 50% of cola drinkers favor Coke over Pepsi? Note:

The Hypothesis Test p = true proportion of all cola drinkers who favor Coke H 0 : p =.5 H A : p >.5  =.05 Reject H 0 if z > z.05 = 1.645

1000 Count the number of alphanumeric observations =COUNTA(A2:A1001) 540 Count the number of “COKE” observations =COUNTIF(A2:A1001, “COKE”).54 x/n =C6/C =(C9-.5)/sqrt((.5*.5)/C5) =1-NORMSDIST(C11)

Review The point estimate for p is: The test statistic, z, is: Use of Excel (COUNTA, COUNTIF Functions)