The owner of a large company is conducting a survey about job satisfaction, including questions about salary, hours, stress, and other conditions. There are about 800 employees in the company, including 100 executive positions, 650 middle-management positions, and 50 custodial positions. The owner wants to include about 10% of his employees in the survey sample.

Identify a sampling method that would lead to a representative sample for the survey. Explain why it would be a good choice and give details about the process.

10% of 800 = 80 total in the sample

Your sample should be based on the ratio of actual positions. Randomly choose 10% of each of the employee categories.

One sampling method that would lead to a representative sample for the survey is stratified random sampling. This method involves dividing the population (in this case, the employees) into meaningful subgroups or strata based on relevant characteristics (in this case, job positions).

In this scenario, the strata would be executive positions, middle-management positions, and custodial positions. The owner wants to include about 10% of the employees in the survey sample, which means approximately 80 employees. Therefore, each stratum should be represented proportionally in the sample.

Here is the process for conducting a stratified random sampling:

1. Identify the strata: In this case, the strata would be executive positions, middle-management positions, and custodial positions.

2. Determine the sample size for each stratum: To maintain proportional representation, the sample size for each stratum should be based on its proportion in the population. In this case, there are 100 executive positions, 650 middle-management positions, and 50 custodial positions. If you want to have approximately 10% of the employees in the sample, you would have around 8 executive positions, 65 middle-management positions, and 5 custodial positions in the sample.

3. Randomly select individuals from each stratum: Within each stratum, individuals should be selected randomly to ensure fairness and avoid bias. You can use a random number generator or a similar method to choose individuals from each stratum.

4. Include selected individuals in the sample: Once the individuals from each stratum are randomly chosen, they should be included in the survey sample.

By using stratified random sampling, the owner ensures that each job position is represented proportionally in the survey sample. This method is appropriate because it allows for comparisons and analysis within each stratum, as well as overall conclusions for the entire company. Additionally, since the owner wants a representative sample that reflects the diversity of employee positions, stratified random sampling is a suitable choice.