Independent Proportions Z-test: Purpose, Hypotheses, and Assumptions

The hypotheses of a two-tailed independent proportions #Z#-test are:

#H_0:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#
#H_a:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#

The hypotheses of a right-tailed independent proportions #Z#-test are:

#H_0:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#
#H_a:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#

The hypotheses of a left-tailed independent proportions #Z#-test are:

#H_0:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#
#H_a:\pi_1 - \pi_2#
#=#
#\neq#
#\gt#
#\lt#
#\geq#
#\leq#

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