Question

a sample of students will be selected from all the students at a high school. which of the following sampling methods is least likely to produce a representative sample of the students? a from a list of all student names, randomly select 50 names from the list for the sample. b randomly choose five classrooms in the school and use all the students in those classrooms for the sample. c divide the students into the four class years (freshman, sophomore, junior, senior) and randomly select students from each year in proportion to the number of students in each year. d from a numbered list of all student names, randomly choose a starting point and then choose every tenth student on the list.

Explanation:

• Option A is simple random - sampling which gives every student an equal chance.
• Option C is stratified sampling, ensuring representation from each class year.
• Option D is systematic sampling which can also be representative if the list is randomly ordered.
• Option B only samples students from 5 randomly chosen classrooms. It may over - represent students in those classrooms and under - represent others, and classroom selection may be biased (e.g., if certain classrooms are used for specific types of classes or have certain types of students).

Answer:

B. Randomly choose five classrooms in the school and use all the students in those classrooms for the sample.