illusiia

2021-02-05

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

izboknil3

Skilled2021-02-06Added 99 answers

Step 1

The two-proportion z-test test method is appropriate when the following criteria are met.

(a)The sampling method for each population is simple random sampling.

(b)The samples are independent.

Step 2

Suppose ${p}_{1}\text{}and\text{}{p}_{2}$ are the proportion of two populations.The hypothesis for comparing the two population proportion is as follows:

Null Hypothesis $({H}_{0}):{p}_{1}-{p}_{2}=0$

According to the null hypothesis, the population proportion is unchanged.

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.

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