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Here are the correct answers and explanations for the given problems:

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**(a)**  
The scenario involves dividing the population into two groups (male and female) and taking separate random samples from each group, then combining them. This is characteristic of **stratified random sampling** because the population is divided into subgroups (strata) and a random sample is taken from each.  
**Answer: B. a stratified random sample.**

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**(b)**  
The population is divided into two distinct groups (men and women), and then separate simple random samples are drawn from each group. This is also an example of **stratified random sampling**, as the division into strata and subsequent random sampling from each is the defining process.  
**Answer: B. stratified random sample.**

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**(c)**  
All the given options essentially define a simple random sample, where every possible sample of size \( n \) has an equal chance of being selected.  
**Answer: D. All of the above. They are essentially identical definitions.**

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### Follow-Up Questions:
1. Why is stratified random sampling more efficient than simple random sampling in certain scenarios?
2. Can you provide examples where systematic sampling would be a better choice than stratified sampling?
3. How does multistage sampling differ from stratified random sampling?
4. What are the advantages of using a simple random sample over other sampling techniques?
5. Could convenience sampling ever be justified in a formal research setting?

**Tip:** Stratified sampling ensures representation from all subgroups, which is particularly useful in heterogeneous populations.

For each problem, select the best response: (a) A small college has 500 male and 600 female undergraduates. A simple random sample of 50 of the male undergraduates is selected, and, separately, a simple random sample of 60 of the female undergraduates is selected. The two samples are combined to give an overall sample of 110 students. The overall sample is... (b) In order to take a sample of 1200 people from a population, I first divide the population into men and women, and then take a simple random sample of 500 men and a separate simple random sample of 700 women. This is an example of... (c) A simple random sample of size n is defined to be...

Explore examples of stratified random sampling and simple random sampling in statistics. Learn about efficient sampling techniques, their definitions, and real-world applications in undergraduate-level studies.

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