Discuss the process to perform hypothesis testing problems about a population proportion using the z statistic.

Hypothesis testing is a way of using data to draw conclusions about the population. When performing hypothesis tests concerning population proportions, the z-statistic should be used. The process for performing a hypothesis test on a population proportion involves five steps: formulating hypotheses, defining level of significance, calculating the value of the test statistic, comparing the test statistic to critical values, and drawing conclusions.

The first step in this process is to formulate null and alternative hypotheses (Ho and Ha). The null hypothesis states that there is no difference between what you would expect if there were no real effect – i.e., Ho: P=p0 where p0 represents your expected parameter value in Ho. The alternative hypothesis states that there is an effect – i.e., Ha: P≠p0 or p>p0 or p
The second step is to define the level of significance as α which determines how likely it will be for us to reject Hₒ after we have calculated our z-statistic from sample data accordingly. Generally speaking, any α less than 0.05 will be accepted as significant since this means that our results will only happen by chance 5% of the time or less when Ho was true all along; if α > 0.05 then we cannot reject Hₒ and must accept Ho as true instead because our results were too likely due to randomness alone so they do not provide enough evidence against Ho being correct in such cases2 .

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