Question

(a) a botanist at a nursery wants to inspect the health of the plants at the nursery. which of the following best describes a random sample of plants?
all of the plants that are in one particular room at the nursery are easily accessible. so, the botanist selects the 60 plants in this particular room.
the botanist forms groups of 12 plants based on the heights of the plants. then, he randomly chooses 5 groups and selects all of the plants in these groups.
the botanist assigns each plant a different number. using a random number table, he draws 60 of those numbers at random. then, he selects the plants assigned to the drawn numbers. every set of 60 plants is equally likely to be drawn using the random number table.
(b) 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 counselors form 4 groups of students based on the numbers of classes the students are taking. then, the counselors select 16 students at random from each group.
the counselors use a computer program to draw 64 students at random and select these students. every set of 64 students is equally likely to be drawn by the computer program.
the counselors form groups of 8 students based on the students’ majors. then, the counselors select all of the students in 8 randomly chosen groups.
(c) the organizers of a conference want to survey attendees about the registration fee. which of the following best describes a convenience sample of attendees?
the organizers form 7 groups of attendees based on the attendees’ employment statuses. then, the organizers select 8 attendees at random from each group.
the organizers select the first 56 attendees who register for the conference because these attendees are easily accessible.
the organizers take a list of the attendees and select every 7th attendee until 56 attendees are selected.

Explanation:

Part (a)

To determine a random sample, we need a method where every set of the desired size (60 plants) has an equal chance of being selected.

• The first option is a convenience sample (selecting easily accessible plants in one room), not random.
• The second option describes cluster sampling (grouping by height, then selecting groups), not simple random.
• The third option: assigning numbers and using a random number table to select 60, with every set equally likely, fits simple random sampling.

A stratified sample involves dividing the population into groups (strata) and then sampling from each group.

• The first option: forming groups by number of classes (strata) and selecting 16 from each group fits stratified sampling.
• The second option is simple random sampling (drawing 64 at random).
• The third option is cluster sampling (grouping by major, then selecting groups).

A convenience sample is selecting individuals who are easily accessible.

• The first option is stratified sampling (grouping by employment status, sampling from each).
• The second option: selecting the first 56 attendees who register (easily accessible) is convenience sampling.
• The third option is systematic sampling (selecting every 7th attendee).

Answer:

The botanist assigns each plant a different number. Using a random number table, he draws 60 of those numbers at random. Then, he selects the plants assigned to the drawn numbers. Every set of 60 plants is equally likely to be drawn using the random number table.

Part (b)