Question

A school principal wants to know what theme students prefer for the spring dance. There are 150 students in the 6th grade, 200 students in the 7th grade, and 187 students in the 8th grade. Select all the representative samples that can help the principal draw conclusions about which themes the students prefer.

A)The students in the 7th grade homerooms

B)The same number of students from each grade whose names are randomly selected from a hat

C)The members of the student council

D)Students who attended the winter dance

E)50 sixth graders, 67 seventh graders, and 62 eighth graders

Answer 1

The representative samples that would provide an accurate reflection of student preferences for the spring dance theme are (B) the same number of students from each grade randomly selected and (E) a fixed number of students from each grade, which is closest to proportional representation.

Step-by-step explanation:

The school principal is seeking representative samples to deduce the preferred theme for the spring dance among students of different grades. The goal is to ensure that the selected sample will provide accurate reflections of the entire population's preferences. When reviewing the options listed, let's identify which represent good sampling methods.

• B) The same number of students from each grade whose names are randomly selected from a hat: This is an example of a stratified random sample, where each stratum (grade level in this case) is represented proportionately. Each grade acts as a separate subgroup, and random sampling within these subgroups ensures that the sample is representative of the entire population.
• E) 50 sixth graders, 67 seventh graders, and 62 eighth graders: Although the numbers are not perfectly proportional to the total numbers in each grade, this approach is closest to a stratified sample where each grade is represented, helping to approximate the composition of the whole population.

Now, let's consider the other options that are not as representative:

• A) The students in the 7th grade homerooms: This selection does not include students from the 6th and 8th grades and therefore is not representative of the entire student body.
• C) The members of the student council: Student council members might not accurately represent the broader student population's preferences, as they are a small and possibly unrepresentative group.
• D) Students who attended the winter dance: This group may have a bias as it only includes students interested in dances, which might not reflect the view of those who didn’t attend.

To summarize, the suitable sampling methods for the principal to use to draw conclusions about the preferred themes for the school dance would be stratified random sampling and ensuring proportional representation from each grade.

Answer 2

B) The same number of students from each grade whose names are randomly selected from a hat

E) 50 sixth graders, 67 seventh graders, and 62 eighth graders

Step-by-step explanation:

B) The reason B is correct is because if all grades get to pick, with the same amount of people from each grade, it would be fair for most, if not all, students.

E) E is correct because of percentages. Let me show you.

6th Grade | 150 Total Students | 50 Students Vote | 33.3% of 150 is 49.95. Round to the nearest whole to get 50.

7th Grade | 200 Total Students | 67 Students Vote | 33.3% of 200 is 66.6. Round to the nearest whole to get 67

8th Grade | 187 Total Students | 62 Students Vote | 33.3% of 187 is 62.271. Round to the nearest whole to get 62.