https://file.aiquickdraw.com/mathbot/file/17293271096551mvysjnr.jpg

Let's break down the problem from the image and match the sampling strategies with their correct techniques:

1. **The researcher gets the complete list from the Census Bureau and uses a computer to randomly select 2000 people.**
   - This describes **Simple Random Sampling** because it involves randomly selecting a sample from the entire population.

2. **The researcher posts the survey on the Internet, the survey question, and waits until 2000 people have responded.**
   - This is **Convenience Sampling** since the researcher is selecting individuals based on their availability and ease of access (those who respond online).

3. **The researcher makes sure that the proportion of respondents from each state matches the proportion of each state's population to the US population.**
   - This is **Stratified Sampling**, where the population is divided into subgroups (strata) and samples are taken to match each subgroup's proportion in the overall population.

4. **The researcher gets the complete list from the Census Bureau and surveys every 1500th person on the list.**
   - This is **Systematic Sampling** since the researcher is selecting every 1500th person from a list, following a set interval.

5. **The researcher picks 20 different small groups: a church group, a Democrat club, a student club, etc., each containing 100 people. Then the researcher makes sure that everyone from each group answers the survey question.**
   - This is **Cluster Sampling**, where the researcher divides the population into clusters (groups) and surveys everyone within the chosen clusters.

Here’s how the answers correspond to the sampling methods:

a. **Convenience Sampling** – Internet survey.
b. **Systematic Sampling** – Every 1500th person.
c. **Cluster Sampling** – 20 different small groups.
d. **Simple Random Sampling** – Randomly selecting from the Census Bureau list.
e. **Stratified Sampling** – Ensuring proportional representation from each state.

Would you like further details or explanations on any of these sampling techniques? 

Here are 5 related questions for practice:
1. What is the main difference between stratified and cluster sampling?
2. How would you ensure a simple random sample is unbiased?
3. What is a potential disadvantage of convenience sampling?
4. How does systematic sampling differ from random sampling?
5. Can stratified sampling be used if the population subgroups are unknown?

**Tip**: In stratified sampling, ensure that the strata are distinct and non-overlapping to avoid sampling bias.

A researcher wants to survey 2000 Americans for an obesity study. Match the strategies to their corresponding sampling techniques.

Learn how to match sampling strategies to techniques in a survey involving 2000 Americans for an obesity study. Explore methods such as simple random sampling, convenience sampling, stratified sampling, and cluster sampling.

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