7 Hypothesis testing for population proportions

In the previous sections, all the problems you encountered involved using population means and sample means. The z-score test can also be used to solve another type of problem – those related to population proportions. Proportions, or relative frequencies, can be determined by dividing the number of items in a specific group or category by the total number of items in the sample. This calculation yields a representation of the quantity of items belonging to a particular group or category, expressed as either a fraction or percentage. In statistical and data analysis, proportions are frequently employed to characterise variable distributions or to contrast distinct groups or categories within a sample.

Figure 29 Data made up

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A pie chart in front of the meeting room. The tag line says ‘86.4% of people will believe any data you put in a PowerPoint side, even it you just totally made it up to prove your point’.

Figure 29 Data made up

Imagine, for example, that a marketing manager surveyed 140 customers and found that 75 customers have been using the company’s service for more than five years. In that case, you can calculate the proportion of loyal customers.

By using the z-score test, you can address the proportion problem by determining the p-value and deciding whether to reject the null hypothesis. Nevertheless, you will need to use a slightly different formula to calculate the z-score for the problem related to population and the sample proportion.

In the next section, you will look at a problem to illustrate this.