In a community of 3000 people, 80 % are Hindus 10 % Muslims, 5 `)/0 Sikh, 4 % Christians and 1 % Jains To select a sample of 300 people to analyses food habits, ideal sample would be –
## Core Concept
The problem revolves around the concept of **stratified sampling**, a method used in statistics to ensure that a sample is representative of the population being studied. This involves dividing the population into distinct subgroups (strata) and then sampling from each subgroup. The goal is to ensure that each subgroup is adequately represented in the sample.
## Why the Correct Answer is Right
The correct answer involves selecting a sample that maintains the same **proportions of religions** as in the total population. Given that the population consists of 80% Hindus, 10% Muslims, 5% Sikhs, 4% Christians, and 1% Jains, an ideal sample of 300 people should reflect these proportions. This means:
- Hindus: 80% of 300 = 0.8 * 300 = 240
- Muslims: 10% of 300 = 0.1 * 300 = 30
- Sikhs: 5% of 300 = 0.05 * 300 = 15
- Christians: 4% of 300 = 0.04 * 300 = 12
- Jains: 1% of 300 = 0.01 * 300 = 3
This distribution ensures that the sample is **representative** of the population's religious demographics.
## Why Each Wrong Option is Incorrect
- **Option A:** Without specific numbers, it's hard to evaluate directly, but any option that does not reflect the proportional representation of the population's religious demographics would be incorrect.
- **Option B:** Similarly, without specifics, if it doesn't match the proportional representation (240 Hindus, 30 Muslims, 15 Sikhs, 12 Christians, 3 Jains), it's incorrect.
- **Option C:** This option would be incorrect for the same reason as A and B; it doesn't provide numbers but would be wrong if it doesn't reflect the population's proportions.
- **Option D:** This is the correct answer based on the provided solution, implying that options A, B, and C do not accurately reflect the proportional representation.
## Clinical Pearl / High-Yield Fact
In **epidemiological studies** and **public health research**, ensuring that a sample is representative of the population is crucial for the validity and generalizability of the findings. Stratified sampling is particularly useful when the population can be divided into subgroups that are thought to be relevant to the study. This method helps in reducing **bias** and increases the **precision** of estimates.
## Correct Answer Line
**Correct Answer: D.**