7 Hypothesis testing for population proportions
In previous sessions, we focused on problems involving population and sample means. However, the z-test has broader applications, including its use in solving problems related to population proportions.
Proportions, also known as relative frequencies, represent the fraction of items in a specific group or category within a larger sample. We calculate proportions by dividing the number of items in a particular group by the total number of items in the sample. This calculation provides a representation of the quantity of items belonging to a specific category, typically expressed as a fraction or percentage.
In the realm of statistical and data analysis, proportions serve several important functions:
- Characterising variable distributions: Proportions help us understand how different categories or values are distributed within a dataset.
- Contrasting distinct groups: By comparing proportions, we can identify differences or similarities between various categories or subsets within a sample.
- Summarising categorical data: Proportions offer a concise way to present information about categorical variables, making it easier to grasp the composition of a dataset.
- Hypothesis testing: We can use proportions to test hypotheses about population parameters, similar to how we use means in other statistical tests.
The application of proportions in statistical analysis allows decision-makers to draw meaningful conclusions about population characteristics based on sample data. This approach proves particularly useful when dealing with categorical variables or when we need to understand the relative occurrence of specific attributes within a population.
The z-test for proportions, specifically, allows us to make inferences about population proportions based on sample data. This test helps determine whether an observed sample proportion differs significantly from a hypothesised population proportion.