Hypothesis testing is a fundamental procedure in statistics, widely used to make inferences about a population based on sample data. When dealing with categorical data, one of the most common applications of hypothesis testing is to test hypotheses about a population proportion. This is particularly useful when we want to test if the proportion of some attribute (e.g., the percentage of people who prefer a particular product, or the proportion of defective items in a manufacturing process) in the population is equal to, greater than, or less than a specific value.

In the context of hypothesis testing about a population proportion, the process generally follows a series of steps, which are outlined below. These steps include defining the hypotheses, selecting the appropriate statistical test, determining the critical region, calculating the test statistic, comparing the test statistic to the critical region, and making a decision regarding the hypothesis.

### 1. State the Null and Alternative Hypotheses

The first step in hypothesis testing is to formulate two competing hypotheses: the null hypothesis (H₀) and the alternative hypothesis (H₁ or Ha).

- Null Hypothesis (H₀): This hypothesis asserts that there is no effect or no difference, and it typically reflects the status quo or a claim that is being tested. In the case of population proportions, the null hypothesis might state that the population proportion is equal to a certain value.
  
  For example:
  \[
  H₀: p = p₀
  \]
  where \( p₀ \) is the hypothesized proportion (e.g., 0.5 for a population where half of the individuals are expected to exhibit a certain characteristic).

- Alternative Hypothesis (H₁ or Ha): This is the hypothesis that reflects a claim contrary to the null hypothesis. The alternative hypothesis might suggest that the population proportion is different from, greater than, or less than the hypothesized value.

  The form of the