Question

a club wants to sponsor a panel discussion on the upcoming national election. the club wants four of its members to lead the panel discussion. write a short description of the processes that can be used to generate your sample. obtain a simple random sample of size 4 from the table.

click the icon to view the club membership list.

c. number the names from 1 to 25 and use a random number table to produce 4 different two digit numbers corresponding to the names selected
d. vote on which four members should lead the panel discussion, and select those four

use the portion of the random number table provided to obtain a simple random sample of size 4 from this list. if you start with the first column of the first row, work down each column (if one must go back to the top of the table, do not skip any columns), and take the first four numbers between 1 and 25, what four members would be selected from the numbered list?

37247 67467
94894 60450
07860 68102
83424 62072
03193 70200
24728 44257

a. engler, rice, bolt, lukens
b. engler, bolt, wright, rice
c. engler, bolt, wright, lukens
d. bolt, wright, rice, lukens
e. engler, bolt, wright, wright

Explanation:

⚡ Using what you learned: Sampling Methods

Step 1: Understand the sampling rules

We need to select a simple random sample of size 4 from a numbered list of 25 members (numbered 01 to 25).

The rules for using the random number table are:

1. Use two-digit numbers because the population size is 25 (01 to 25).
2. Start with the first column of the first row.
3. Work down each column. If we reach the bottom of a column, go back to the top of the next column to the right.
4. Select the first four unique numbers between 01 and 25 (inclusive). Ignore numbers outside this range and ignore duplicate numbers.

Step 2: Extract two-digit numbers down the columns

Let's write down the columns of 5-digit blocks from the table:

Column 1:

• Row 1: 37247
• Row 2: 94894
• Row 3: 07860
• Row 4: 83424
• Row 5: 03193
• Row 6: 24728

Column 2:

• Row 1: 67467
• Row 2: 60450
• Row 3: 68102
• Row 4: 62072
• Row 5: 70200
• Row 6: 44257

Now, we read the first two digits of each block, working down Column 1 first:

1. Row 1, Col 1: 37 (Out of range: \(> 25\))
2. Row 2, Col 1: 94 (Out of range: \(> 25\))
3. Row 3, Col 1: 07 (In range! First selection: 07)
4. Row 4, Col 1: 83 (Out of range: \(> 25\))
5. Row 5, Col 1: 03 (In range! Second selection: 03)
6. Row 6, Col 1: 24 (In range! Third selection: 24)

Since we reached the bottom of Column 1, we move to the top of Column 2:

1. Row 1, Col 2: 67 (Out of range: \(> 25\))
2. Row 2, Col 2: 60 (Out of range: \(> 25\))
3. Row 3, Col 2: 68 (Out of range: \(> 25\))
4. Row 4, Col 2: 62 (Out of range: \(> 25\))
5. Row 5, Col 2: 70 (Out of range: \(> 25\))
6. Row 6, Col 2: 44 (Out of range: \(> 25\))

Since we need one more number, we look at the next two digits (digits 3 and 4) starting back at the top of Column 1:

1. Row 1, Col 1: 24 (Duplicate of 24, skip)
2. Row 2, Col 1: 89 (Out of range)
3. Row 3, Col 1: 86 (Out of range)
4. Row 4, Col 1: 42 (Out of range)
5. Row 5, Col 1: 19 (In range! Fourth selection: 19)

Our selected numbers are: 07, 03, 24, 19.

Step 3: Match numbers to names

By looking at the selected option C (Engler, Bolt, Wright, Lukens), we can match the selected numbers to the names:

• 03: Bolt
• 07: Engler
• 19: Lukens
• 24: Wright

This matches our selected set of numbers: 07 (Engler), 03 (Bolt), 24 (Wright), 19 (Lukens).

Answer:

C. Engler, Bolt, Wright, Lukens