Question

The United States Senate has 2 senators from each of the 50 states. Select all methods that would select a sample of 10 senators at random from the entire Senate.

A) Take the 10 senators from the 5 largest states.
B) Take the 10 senators who have served in the Senate the longest.
C) Place the names of all 100 senators on individual slips of paper placed into a bowl. Thoroughly mix up the slips and then select 10 of them.
D) Send letters to all 100 senators. Select the 10 that reply back the quickest.
E) Number the senators from 1 to 100. Use a random number generator to make a list of 10 random integers between 1 and 100 inclusive.

Answer 1

To randomly select a sample of 10 senators, place names on slips of paper and draw 10 (Option C), or use a random number generator to select 10 numbers representing senators (Option E). Other listed options are not random.

Step-by-step explanation:

The question concerns the selection of a sample of 10 senators at random from the entire United States Senate, which is composed of 100 members, with two senators from each of the 50 states. To select a sample at random, the process must give all members an equal chance of being chosen. The methods that would accomplish this are:

• Option C: Place the names of all 100 senators on individual slips of paper, mix them thoroughly in a bowl, and then select 10 slips.
• Option E: Assign numbers from 1 to 100 to each senator and use a random number generator to select 10 unique random integers within this range.

Options A, B, and D would not be considered random sampling methods. Selecting senators from the 5 largest states or those who have served the longest introduces a bias, as does selecting the first 10 senators to reply to letters.