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Let's address the questions from your assignment on the principles of sampling.

### 1. Difference Between Population and Sample
- **Population** refers to the entire group of individuals or items that you are interested in studying. In this context, the population consists of all 3000 people from the 5 different sections in the barangay.
- **Sample** is a smaller, manageable subset of the population selected for the study. The sample should be representative of the population to allow for accurate generalizations.

### 2. Stratified Sampling Method
To use the **stratified sampling method** with a 5% margin of error, follow these steps:

1. **Determine the Sample Size for Each Section**: 
   - A 5% sample size from the total population (3000 people) is calculated as:
   \[
   \text{Total Sample Size} = \text{Total Population} \times 0.05 = 3000 \times 0.05 = 150.
   \]
   - Distribute the sample size proportionally based on the population of each section (Purok 1 to Purok 5). The formula for each section is:
   \[
   \text{Sample per Section} = \left( \frac{\text{No of students in the section}}{\text{Total Population}} \right) \times \text{Total Sample Size}.
   \]

2. **Calculate Sample Size for Each Section:**
   - For **Purok 1**: 
   \[
   \frac{660}{3000} \times 150 \approx 33.
   \]
   - For **Purok 2**: 
   \[
   \frac{520}{3000} \times 150 \approx 26.
   \]
   - For **Purok 3**: 
   \[
   \frac{750}{3000} \times 150 \approx 38.
   \]
   - For **Purok 4**: 
   \[
   \frac{590}{3000} \times 150 \approx 30.
   \]
   - For **Purok 5**: 
   \[
   \frac{480}{3000} \times 150 \approx 24.
   \]

3. **Verify Total Sample Size:**
   \[
   33 + 26 + 38 + 30 + 24 = 151.
   \]
   (Due to rounding, the total is slightly above 150, but this is acceptable.)

### 3. Minimum Sample Size for Cluster Sampling
To determine the minimum sample size for **cluster sampling**, you generally select entire clusters (in this case, sections) randomly. The minimum sample size would depend on the variability within clusters and the required precision or confidence level. For simplicity, you could consider sampling at least 1-2 clusters fully, but a detailed statistical analysis would be needed for an exact number.

Would you like further details on this solution, or do you have any additional questions? Here are some follow-up questions to consider:

1. How does stratified sampling differ from simple random sampling?
2. What are the advantages of using stratified sampling in this case?
3. How do you calculate the margin of error in sampling?
4. What factors should be considered when choosing a sampling method?
5. How does cluster sampling reduce costs compared to other sampling methods?

**Tip:** When calculating a sample size, always consider the population's heterogeneity to ensure the sample represents the population accurately.

What is the difference between population and sample? A sample has to be drawn from a barangay from 5 puroks composed of 3000 populations as shown in the table below. How will you draw the sample using stratified sampling method, using 5% margin of error? Show the solution and the sample you will get per section. What would be the minimum sample size if you are to use cluster sampling?

Learn how to calculate sample sizes using stratified sampling methods with a 5% margin of error. The problem focuses on sampling from a barangay with 5 puroks, covering core concepts such as population, sample size, stratified sampling, and cluster sampling.

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