1. **Stating the problem:** A Human Resource Manager wants to sample employees from 5 different departments to gauge engagement levels. Each department has a different number of employees. 2. **Understanding sampling methods:** There are several sampling methods in statistics, including: - **Simple Random Sampling:** Every employee has an equal chance of being selected. - **Stratified Sampling:** The population is divided into subgroups (strata) like departments, and samples are taken from each proportionally. - **Cluster Sampling:** Entire groups or clusters (e.g., departments) are randomly selected. - **Systematic Sampling:** Selecting every k-th employee from a list. 3. **Choosing the appropriate method:** Since the organisation has 5 departments with different numbers of employees, and the manager wants to represent all departments, **Stratified Sampling** is the best choice. 4. **Formula and explanation:** In stratified sampling, the sample size from each department is proportional to its size: $$ n_i = \frac{N_i}{N} \times n $$ where: - $n_i$ = sample size from department $i$ - $N_i$ = number of employees in department $i$ - $N$ = total number of employees - $n$ = total desired sample size 5. **Why stratified sampling?** It ensures representation from all departments, especially important when department sizes vary. This reduces sampling bias and improves accuracy. 6. **Summary:** Use **Stratified Sampling** by dividing employees into 5 strata (departments) and sampling proportionally from each.