A researcher wants to select a random sample of 200 companies from out of all the companies from manufacturing sector, pharmaceutical sectors, automobile sectors and ‘others’. Suggest a suitable sampling method she may use and explain how she Should proceed to select the sample

To select a random sample of 200 companies from the manufacturing, pharmaceutical, automobile, and "other" sectors, a **stratified random sampling** method would be suitable. This method is useful when the population can be divided into distinct subgroups (strata) — in this case, the different sectors. Stratified sampling ensures that each sector is adequately represented in the sample, which may be important if the researcher wants to generalize findings to all companies in each sector.

Here’s how the researcher should proceed with stratified random sampling:

### 1. **Identify Strata (Sectors):**
   The population (all companies) can be divided into four strata based on their sector:
   - Manufacturing
   - Pharmaceutical
   - Automobile
   - Others

### 2. **Determine the Proportion of Each Stratum:**
   Determine the proportion of companies in each sector (stratum) relative to the total population. For example, if 40% of the companies are in the manufacturing sector, 30% in pharmaceutical, 20% in automobile, and 10% in others, these proportions should guide the sample size from each stratum.

### 3. **Calculate Sample Sizes for Each Stratum:**
   Using the proportions from step 2, calculate how many companies to sample from each stratum. For example, if the researcher needs 200 companies and 40% of the population is from the manufacturing sector, then \( 0.4 \times 200 = 80 \) companies should be sampled from the manufacturing sector.
   - Manufacturing: \(0.4 \times 200 = 80\)
   - Pharmaceutical: \(0.3 \times 200 = 60\)
   - Automobile: \(0.2 \times 200 = 40\)
   - Others: \(0.1 \times 200 = 20\)

### 4. **Randomly Select Companies from Each Stratum:**
   After calculating the number of companies to sample from each sector, use **simple random sampling** to randomly select the required number of companies from each stratum. This can be done using a random number generator or other randomization tools.

### 5. **Combine the Samples:**
   Finally, combine the samples from each stratum to form the overall sample of 200 companies.

### Benefits of Stratified Sampling:
- **Representation**: It ensures that all sectors are represented proportionally.
- **Reduced Bias**: Random sampling within each stratum minimizes selection bias.
- **Increased Precision**: By sampling proportionally from each sector, the sample is more likely to be representative of the entire population, which increases the precision of the research findings.

### Alternative Methods:
If the proportions of companies in each sector are unknown or irrelevant, **simple random sampling** could be used directly from the entire population without dividing into sectors.

Would you like further details on stratified sampling or another method?

---

Here are 5 related questions you could explore:
1. How can you determine the exact proportion of companies in each sector?
2. What are the advantages of stratified sampling over cluster sampling?
3. How does stratified sampling help reduce sampling bias?
4. What are some limitations of stratified random sampling in practice?
5. Can stratified sampling be used for non-proportional sampling? If yes, when?

**Tip:** When performing stratified sampling, always ensure that each group or stratum is mutually exclusive and collectively exhaustive. This prevents any company from being included in multiple strata or left out.

A researcher wants to select a random sample of 200 companies from out of all the companies from manufacturing sector, pharmaceutical sectors, automobile sectors and ‘others’. Suggest a suitable sampling method she may use and explain how she should proceed to select the sample.

Learn how to use stratified random sampling to select a random sample of 200 companies from the manufacturing, pharmaceutical, automobile, and other sectors. This method ensures proportional representation and reduces bias in the research findings. Ideal for undergraduate or graduate students studying statistics or research methods.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation