Question

(a) counselors at a college want to poll students about how much time the students spend studying. which of the following best describes a stratified sample of students?
the students living in a particular dorm building on campus are easily accessible. so, the counselors select the 80 students living in that particular dorm building.
the counselors take a list of the students and select every 4th student until 80 students are selected.
the counselors form 4 groups of students based on the numbers of classes the students are taking. then, the counselors select 20 students at random from each group.

(b) a chemist at a pharmaceutical company wants to test the quality of a new batch of microscopes. which of the following best describes a convenience sample of microscopes?
the chemist forms groups of 30 microscopes based on the laboratories that the microscopes are in. then, he randomly chooses 3 groups and selects all of the microscopes in these groups.
the microscopes in the first shipment that was received are easily accessible. so, he selects all 90 of the microscopes in this shipment.
the chemist assigns each microscope a different number. using a random number table, he draws 90 of those numbers at random. then, he selects the microscopes assigned to the drawn numbers. every set of 90 microscopes is equally likely to be drawn using the random number table.

(c) the organizers of a conference want to survey attendees about the registration fee. which of the following best describes a cluster sample of attendees?
the organizers form groups of 8 attendees based on the day the attendees registered. then, the organizers randomly choose 9 groups and select all of the attendees in these groups.
the organizers form 6 groups of attendees based on the attendees employment statuses. then, the organizers select 12 attendees at random from each group.
the organizers take a list of the attendees and select every 3rd attendee until 72 attendees are selected.

Explanation:

Part (a)

A stratified sample involves dividing the population into groups (strata) and then taking a random sample from each group. Here, the counselors form 4 groups based on the number of classes (strata) and select 20 students from each group, which matches the definition of a stratified sample. The first option is a convenience sample (easy access), the second is a systematic sample (every 4th student).

A convenience sample is a sample where participants are selected because they are easily accessible. The chemist selects all microscopes from the first shipment (easily accessible), so this is a convenience sample. The first option is a cluster sample (groups and selecting all in chosen groups), the third is a simple random sample (random number table).

A cluster sample involves dividing the population into clusters, randomly selecting some clusters, and then including all members of the selected clusters. The organizers form groups (clusters) based on registration day, randomly choose 9 groups, and select all attendees in those groups, which is a cluster sample. The second option is stratified (selecting from each group), the third is systematic (every 3rd attendee).

Answer:

The counselors form 4 groups of students based on the numbers of classes the students are taking. Then, the counselors select 20 students at random from each group.

Part (b)