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

Question

Answer 1

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 $p_{1} a n d p_{2}$ are the proportion of two populations.The hypothesis for comparing the two population proportion is as follows:
Null Hypothesis $(H_{0}) : p_{1} - p_{2} = 0$
The null hypothesis state that there is no difference in population proportion
Alternative Hypothesis $(H_{1}) : p_{1}$ 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:
$z = \frac{p_{1} - p_{2}}{\sqrt{p (1 - p) (\frac{1}{n_{1}} + \frac{1}{n_{2}})}}$
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.

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

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