3 Homework Question 6, 1,3,13 pritt of? IW Seores selk 120 d 28 ponts Dontsoods services. The administration provides you with a list of the names and phone numbers of the 701 ropatered students (a) Discuss a procedure you could follow to obtain a simple random sample of 5 atudents. (b) Obtain this sample. Click the tcon to $$ v $$ tew the portion of the random number table. (a) Which of the following procedures could you follow to obtain a simple random sample of 5 students? Select all that apply- A. List the names in alphabetical order and take the first five names on the list. B. List each name on a separate piece of paper; place them all in a hat, and pick five. C. Ask the students to come to a meeting and pick five from those who come to the meeting. D. Number the names from 1 to 701 and use a random number table to produce 5 different three-digit numbers corresponding to the names selected.

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UpStudy AI · Accepted Answer

Sure, let's break down **Question 6** and address each part systematically.

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### **Question 6(a): Discuss a procedure you could follow to obtain a simple random sample of 5 students.**

**Answer:**

To obtain a **simple random sample** of 5 students from a population of 701, you can follow these steps:

1. **Assign Unique Numbers:**
   - Assign a unique identifier (e.g., numbers from 001 to 701) to each of the 701 students. This ensures that every student has an equal chance of being selected.

2. **Use a Random Selection Method:**
   - **Random Number Table:** Utilize a random number table to generate 5 unique numbers within the range of 001 to 701.
   - **Random Number Generator:** Alternatively, use software or an online random number generator to produce 5 unique numbers within the same range.
   
3. **Select the Sample:**
   - Match the randomly generated numbers to the corresponding student identifiers. The students associated with these numbers constitute your simple random sample of 5.

**Example Procedure:**

1. **List Assignment:**
   - Number all students from 001 to 701.

2. **Random Selection:**
   - Suppose the random number generator selects 045, 289, 502, 613, and 710.
   
3. **Sample Identification:**
   - Identify and select the students corresponding to these numbers as your sample.

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### **Question 6(b): Obtain this sample.**

**Answer:**

Since I don't have access to the actual list of student names and their assigned numbers, I'll illustrate how you would obtain the sample using a **random number table**. Here's a hypothetical example:

1. **Assume the Students are Numbered from 001 to 701.**

2. **Using a Random Number Table:**
   - Suppose you consult a random number table and extract the following five unique three-digit numbers within the range:
     - **123**
     - **456**
     - **789** (Note: Since our range is up to 701, if a number like 789 appears, you'd skip it and select the next valid number.)
     - **234**
     - **567**

3. **Valid Sample Numbers:**
   - Adjusting for the valid range, let's say the selected numbers are:
     - **123**, **456**, **234**, **567**, and **678**.

4. **Identifying Students:**
   - Match these numbers to the corresponding students on your list. These five students are your simple random sample.

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### **Multiple-Choice Question:**

**Which of the following procedures could you follow to obtain a simple random sample of 5 students? Select all that apply.**

- **A.** List the names in alphabetical order and take the first five names on the list.
- **B.** List each name on a separate piece of paper, place them all in a hat, and pick five.
- **C.** Ask the students to come to a meeting and pick five from those who come to the meeting.
- **D.** Number the names from 1 to 701 and use a random number table to produce 5 different three-digit numbers corresponding to the names selected.

**Correct Options:** **B and D**

**Explanation:**

- **Option A:** *Not Correct.* Selecting the first five names from an alphabetically ordered list introduces bias, as it's not a random selection method.
  
- **Option B:** *Correct.* Placing each student's name in a hat and randomly picking five ensures that every student has an equal chance of being selected, making it a simple random sample.
  
- **Option C:** *Not Correct.* This method relies on self-selection, meaning only students who choose to attend the meeting are eligible for selection, which can introduce bias.
  
- **Option D:** *Correct.* Numbering each student and using a random number table to select numbers ensures randomness and that each student has an equal probability of being chosen.

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### **Summary:**

- **For obtaining a simple random sample:** Assign unique identifiers and use a random selection method (like a random number table or generator).
  
- **For the multiple-choice question:** **Options B and D** are valid procedures for obtaining a simple random sample of 5 students.

If you have access to the random number table and the list of student numbers, you can proceed with part (b) by selecting the corresponding students based on the randomly generated numbers.
To obtain a simple random sample of 5 students from 701: 1. **Assign each student a unique number from 1 to 701.** 2. **Use a random number table or generator to select 5 unique three-digit numbers within this range.** 3. **Select the students corresponding to these numbers.** **Example:** - Random numbers: 123, 456, 234, 567, 678 - Sample students: Students with numbers 123, 456, 234, 567, 678 **Multiple-Choice Answer:** - **B.** List each name on a separate piece of paper, place them all in a hat, and pick five. - **D.** Number the names from 1 to 701 and use a random number table to produce 5 different three-digit numbers corresponding to the names selected. These methods ensure each student has an equal chance of being selected.

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