# Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.

Explain the basic idea for performing a hypothesis test, based on independent samples, to compare two population proportions.
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Step 1
The test procedure, called the two-proportion z-test, is appropriate when the following conditions are met
(a)The sampling method for each population is simple random sampling.
(b)The samples are independent.
Step 2
Suppose are the proportion of two populations.The hypothesis for comparing the two population proportion is as follows:
Null Hypothesis $\left({H}_{0}\right):{p}_{1}-{p}_{2}=0$
The null hypothesis state that there is no difference in population proportion
Alternative Hypothesis $\left({H}_{1}\right):{p}_{1}$ is not equal to ${p}_{2}$.
The alternative hypothesis state that there is a significant difference between proportions.
Step 3
The test statistic is defined is as follows:
$z=\frac{{p}_{1}-{p}_{2}}{\sqrt{p\left(1-p\right)\left(\frac{1}{{n}_{1}}+\frac{1}{{n}_{2}}\right)}}$
Where,
$p=\frac{{n}_{1}{p}_{1}+{n}_{2}{p}_{2}}{{n}_{1}+{n}_{2}}$
Decision rule:
If the test statistic is greater than z- critical. Reject the null hypothesis.