Question

algebra 2 hw 5.03 (due 1/09) name
1 andre is in the band and he is conducting an experiment to determine if high school students find listening to classical music or listening to the sounds of the ocean more calming. he selects five students at random from the band to listen to classical music. he then selects five people at random from the swim team to listen to the sounds of the ocean. what is problematic about the way that andre selected his groups?

1. you want to survey twenty of the 150 ninth graders to get their opinion on the school’s new schedule. which of the following methods is most likely to lead to a sample that is the most representative of the 150 ninth graders?

a. choose 20 ninth graders from your first period class.

b. choose the first 20 ninth graders from an alphabetical list.

c. select 20 students at random from the ninth grade.

d. select 5 students at random from each of ninth, tenth, eleventh and twelfth grade.

1. 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.

go to back

Explanation:

Question 1

Andre's sampling is problematic because he selected participants from specific groups (band and swim team) instead of a random or representative sample of all high school students. This introduces bias as these groups may have different characteristics (e.g., band students might have different music preferences) that could affect the results, making the sample unrepresentative of the target population (all high school students).

To get a representative sample, random sampling from the entire population (ninth - grade students) is best. Option a (first - period class) is biased as it's a specific class. Option b (first 20 from alphabetical list) may have bias (e.g., name - related). Option d samples from multiple grades, not just ninth. Option c (random selection from ninth grade) gives each ninth - grader an equal chance, minimizing bias.

• Option a: Sampling from the 5 largest states is biased (not random).
• Option b: Sampling by longest service is biased (not random).
• Option c: Randomly selecting from all 100 senators' names is a simple random sample, random.
• Option d: Selecting those who reply quickest is biased (favors those with more time/interest).
• Option e: Using a random number generator to select from numbered senators is a random sampling method.

Answer:

Andre's sample is unrepresentative as he selected from specific groups (band, swim team) instead of a random/representative sample of all high school students, introducing bias.

Question 2