Chapter 8. Testing for Differences in Mean and Proportion: Independent Proportions Ztest
Independent Proportions Ztest: Purpose, Hypotheses, and Assumptions
Independent proportions Ztest: Purpose and Hypotheses
The independent proportions #\boldsymbol{Z}#test is used to test hypotheses about the difference between two population proportions #\pi_1  \pi_2#.
Specifically, the test is used to determine whether or not it is plausible that #\pi_1\pi_2# differs from some value #\Delta#. In most situations #\Delta=0#, so we will only present this specific setting.
The hypotheses of a independent proportions #Z#test are:
Twotailed#^1#  Lefttailed  Righttailed 



Assumptions of the Independent proportions Ztest
The following assumptions are required to hold in order for an Independent proportions #Z#test to produce valid results:
 Random sampling is used to draw the samples.
 Independence of observations, meaning:
 No individual can be part of both samples.
 No individual in either sample can influence individuals in the same sample.
 No individual in either sample can influence individuals in the other sample.
 The sampling distribution of the difference between the sample proportions is approximately normal.
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