https://file.aiquickdraw.com/mathbot/file/1728083941943dojciq49.jpg

Let's analyze and solve each question presented in the image.

### (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":

- This sampling process involves separating the population into groups (males and females) and then taking random samples from each group. This is a **stratified random sampling**, where the population is divided into strata (here, gender), and then random samples are taken from each stratum.

**Answer: E. a stratified random sample.**

### (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 a":

- Again, the population is divided into two groups (men and women), and simple random samples are taken from each group. This is another example of **stratified random sampling**, as the population is first divided into groups (strata), and then simple random samples are drawn from each group.

**Answer: E. stratified random sample.**

### (c) "A simple random sample of size \(n\) is defined to be":

1. **A sample of size \(n\) chosen in such a way that every set of \(n\) units in the population has an equal chance to be the sample actually selected.**
2. **A sample of size \(n\) chosen in such a way that every unit in the population has the same chance of being selected.**
3. **A sample of size \(n\) chosen in such a way that every unit in the population has a known nonzero chance of being selected.**

- All three options are consistent definitions of a simple random sample. Thus, the correct answer is:

**Answer: D. All of the above.**

---

Would you like further explanation or details on any of these concepts? Here are 5 related questions to expand on the topic:

1. What is the difference between stratified sampling and cluster sampling?
2. Can stratified sampling be used for non-homogeneous populations? Why or why not?
3. How does multistage sampling differ from stratified sampling?
4. What are the advantages of using a stratified random sample over a simple random sample?
5. In what situations would convenience sampling be preferable, despite its limitations?

**Tip:** Stratified sampling helps ensure that specific subgroups (like gender, age, or income level) are represented proportionally in a study.

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:

Understand how to perform stratified sampling in a population of male and female undergraduates. This problem involves selecting a simple random sample from different strata and combining them. Suitable for students learning about sampling techniques in statistics.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation