Hypothesis tests for two or more proportions

The research question of interest in some studies can be phrased Does the test treatment result in a higher probability of attaining a desired state than the control Examples of such applications include  

In a confirmatory trial of an antihypertensive, for example, a sponsor might like to know if the test treatment results in a higher proportion of hypertensive individuals (which can be interpreted as a probability) reaching an SBP 140 mmHg. 

In the case of a hypothesis test for two proportions the null and alternate statistical hypotheses can be stated as follows  

The sample proportions will be used to estimate the population proportions and, as in Chapter 8, are defined as  

The estimator for the difference in the two sample proportions is pj -p and the standard error of the difference pj -p is  

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Hypothesis test for two (or more) proportions y test of homogeneity... 

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