Question

Leewood Middle School is considering a uniform policy, and the principal has asked for students' opinions about the colors for the uniform shirts. Jennifer and Josef conducted surveys about the possible shirt colors. Their methods and results are described below. Jennifer · Sampling method: Gave each student in her history class a survey to complete anonymously at home and return the following day. She received 50% of the surveys the next day. · Results: 85% prefer blue shirts. Josef · Sampling method: Wrote all students' names on slips of paper. Gave survey to the 50 students whose names were chosen at random. · Results: 60% prefer blue shirts.

Explain whose sampling method will provide results most representative of all students at Leewood Middle School and why. Provide your own example of another method that would represent all students at Leewood Middle School.

Answer 1

Josef’s random sampling method provides more representative results of the student population at Leewood Middle School than Jennifer’s class-limited survey. A stratified sampling method, involving proportional selection from different grades, would also ensure a representative sample.

Step-by-step explanation:

The student who will provide results most representative of all students at Leewood Middle School is Josef. Josef's sampling method involves randomly selecting students, which ensures each student has an equal chance of being included in the survey. This approach minimizes bias and is considered more reliable than Jennifer's approach which was limited to her history class, potentially skewing the results based on the specific demographic or opinions of that class.

An alternative method that would provide a representative sample of all students at Leewood Middle School could be stratified sampling. This would involve dividing the entire school population into different subgroups, or 'strata', such as grade level or any other relevant characteristic, and then randomly selecting students from each subgroup to participate in the survey. This ensures that all segments of the student population are adequately represented.

Here is an example: If Leewood Middle School has grades 6 to 8, the school could first identify the total number of students in each grade. Then, use random sampling to select a proportional number of students from each grade to participate in the survey about uniform colors.