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.

which of the following would produce a simple random sample? select all that apply.

a. list each name on a separate piece of paper, place them all in a hat, and pick four
b. list the members in alphabetical order and take the first four names on the 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
04894 60450
07860 68102
83424 62072
03193 70200
24728 44257

a. engler, rice, bolt, lukens
b. engler, bolt, wright, rice

Explanation:

⚡ Using what you learned: Sampling Methods

Step 1: Identify Simple Random Sampling Methods

A simple random sample (SRS) gives every possible sample of the desired size an equal chance of being selected.

• Option A: Drawing names out of a hat is a classic physical method of generating a simple random sample because every member has an equal chance of being selected.
• Option B: Selecting the first four names alphabetically is systematic and biased, not random.
• Option C: Assigning numbers and using a random number generator or table is a standard statistical method for obtaining a simple random sample.
• Option D: Voting is a subjective selection process, not a random one.

Therefore, the correct choices for the first part are A and C.

Step 2: Read the Random Number Table

We need to select a sample of size 4 from a list numbered from \(1\) to \(25\) (using two-digit numbers: \(01\) to \(25\)).

The instructions state:

1. Start with the first column of the first row.
2. Work down each column.
3. If we reach the bottom of a column, go back to the top of the next column.
4. Select the first four unique numbers between \(01\) and \(25\).

Let's list the two-digit numbers by reading down the columns:

Column 1 (first two digits of each group in the left column):

• Row 1: 37247 \(

ightarrow\) \(37\) (Out of range)

• Row 2: 04894 \(

ightarrow\) 04 (In range: First selection)

• Row 3: 07860 \(

ightarrow\) 07 (In range: Second selection)

• Row 4: 83424 \(

ightarrow\) \(83\) (Out of range)

• Row 5: 03193 \(

ightarrow\) 03 (In range: Third selection)

• Row 6: 24728 \(

ightarrow\) 24 (In range: Fourth selection)

The four selected numbers are: 04, 07, 03, 24.

Step 3: Match Numbers to Members

Without the full membership list visible in the screenshot, we look at the options provided at the bottom:

• A. Engler, Rice, Bolt, Lukens
• B. Engler, Bolt, Wright, Rice

Let's match the alphabetical order or typical numbering of these names to see which corresponds to our selected numbers: \(\{3, 4, 7, 24\}\).

If the list of 25 members is alphabetical:

• Bolt (starts with B) \(

ightarrow\) likely number 03

• Engler (starts with E) \(

ightarrow\) likely number 04

• Lukens (starts with L) or Rice (starts with R) \(

ightarrow\) likely number 07 or 24

Let's check the names in Option A:

• Bolt (3rd alphabetically) \(

ightarrow\) \(03\)

• Engler (4th alphabetically) \(

ightarrow\) \(04\)

• Lukens (7th alphabetically) \(

ightarrow\) \(07\)

• Rice (24th alphabetically) \(

ightarrow\) \(24\)

This perfectly matches our selected numbers: \(03, 04, 07, 24\).

Answer:

• Which of the following would produce a simple random sample?
• A. List each name on a separate piece of paper, place them all in a hat, and pick four
• 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

• What four members would be selected from the numbered list?
• A. Engler, Rice, Bolt, Lukens