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Security awareness training Of 400 employees at a company, \(25 \%\) work in production, \(40 \%\) work in sales and marketing, and \(35 \%\) work in new product development. As part of a security awareness training program, the group overseeing implementation of the program will randomly choose a sample of 20 employees to begin the training; the percentages of workers from each department in the sample are to align with the percentages throughout the company. a. What type of sampling could be used to achieve this goal? b. Explain how to carry out the sampling using a table of random digits.

Short Answer

Expert verified
Use stratified sampling, ensuring the sample size matches department percentages. For each department, randomly select employees using a random digit table until the quota is met.

Step by step solution

01

Identify Sampling Type

The goal is to ensure the sample reflects the same proportions as the entire company's workforce across departments. This requires a type of sampling called 'Stratified Sampling'. In stratified sampling, we divide the population into distinct subgroups (strata) based on a characteristic (here, department) and then sample from each subgroup proportionately.
02

Calculate Number of Employees Per Department

Since 25% of employees work in production, calculate the number of production workers in the sample as follows: \(25\% \times 20 = 0.25 \times 20 = 5\) employees. Similarly, for sales and marketing, \(40\% \times 20 = 0.40 \times 20 = 8\) employees, and for product development, \(35\% \times 20 = 0.35 \times 20 = 7\) employees.
03

Prepare Sampling Frame

Prepare a list of employees in each department. Ensure each employee has a unique identification number within their department. For example, number production workers 1 to 100, sales and marketing workers 101 to 260, and product development workers 261 to 400.
04

Use Table of Random Digits

To select employees using a table of random digits, start by choosing a random starting point in the table. Read two-digit numbers sequentially to avoid bias. Select numbers that match the identification numbers of employees until reaching the required count for each department. Repeat separately for each department to ensure stratification.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Sampling Methods
Sampling methods are different techniques used to select a subset of a population for study. Understanding the right sampling method is crucial to ensure that the sample accurately represents the whole group and to minimize bias.
There are various sampling methods to choose from, including simple random sampling, systematic sampling, stratified sampling, and cluster sampling. Each method has its own advantages and is suited for different types of studies.
In the context of the security awareness training exercise, **stratified sampling** is the most appropriate method. This method involves dividing the entire population into distinct subgroups or 'strata' based on certain characteristics, such as department. Then, a sample is drawn randomly from each subgroup in a way that maintains the population proportions. This ensures that all significant subgroups are represented adequately in the sample, making stratified sampling highly precise and reliable for this scenario.
Proportional Allocation
Proportional allocation is a technique used in stratified sampling to ensure each subgroup in a population is represented fairly in the sample.
For the company's employee training program, proportional allocation requires calculating the number of employees to sample from each department based on the department’s share of the total workforce.
Here's how it looks:
  • Production makes up 25% of the workforce, so 25% of the sample (5 employees) should be from production.
  • Sales and marketing make up 40%, so they should have 40% of the sample (8 employees).
  • Product development covers the remaining 35%, needing 35% of the sample (7 employees).
Proportional allocation helps ensure that the sample mirrors the population's structure, providing more accurate and credible results.
Random Sampling
Random sampling is a fundamental concept within sampling methods where each member of a population has an equal chance of being selected.
When conducting a random sampling, you can use tools like a table of random digits to help ensure that the selection process is impartial and free from any bias.
In a stratified random sampling scenario, after dividing the entire population into strata, random sampling is used within each subgroup to choose the participants. For instance, for the training program, employees who belong to the production department are chosen randomly, as are those in sales and marketing and product development. Using a table of random digits helps create a transparent and unbiased selection process.
Data Collection Techniques
Data collection techniques are methods used to gather information from participants effectively and efficiently.
Using stratified sampling, as in the security awareness training example, involves carefully organizing information about the population—such as employee departments—and collecting data that reflects this arrangement.
To employ a table of random digits for data collection:
  • First, assign unique identification numbers to each employee within their respective department.
  • Next, select a starting point in the table and read numbers sequentially to randomly pick employees.
  • Ensure the number matches the department's ID numbers until the desired sample size is reached.
This systematic approach to data collection ensures randomness, reducing biases and improving the reliability of the data obtained.

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