Question

a botanist wants to inspect the health of the plants at the nursery. which of the following best describes a cluster sample of plants?
(a) a botanist wants to inspect the health of the plants at the nursery. so, the botanist selects the 72 plants in one particular room at the nursery because they are easily accessible. then, he randomly chooses 9 groups and selects all of the plants in this particular room.
(b) a bank analyst wants to ask customers who have a mortgage with the bank about the customers home - buying experiences. which of the following best describes a stratified sample of customers?
the analyst forms 6 groups of customers based on the customers mortgage amounts. then, she selects 13 customers at random from each group.
the analyst forms 6 groups of customers based on the customers mortgage amounts. then, she selects the first 78 customers who answer because these customers are easily accessible.
the analyst spends a day calling mortgage customers and selects the first 78 customers who answer because these customers are easily accessible.
the analyst forms 13 groups of customers based on the cities the customers live in. then, she selects all of the customers in 6 randomly chosen groups.
(c) a facilities supervisor at a sports stadium wants to rate the condition of the seats at the stadium. which of the following best describes a systematic sample of seats?
the supervisor forms 5 groups of seats based on the dates the seats were last replaced. then, she selects 18 seats at random from each group.
the supervisor uses a computer program to draw 90 seats at random and selects these seats. every set of 90 seats is equally likely to be drawn.
the supervisor takes a list of the seats and selects every 5th seat until 90 seats are selected.

Explanation:

Part (a)

To identify cluster sampling, we recall that cluster sampling involves dividing the population into clusters (groups) and then randomly selecting some clusters, and including all members of the selected clusters. Here, the botanist divides the plants into groups (clusters) by the room (one particular room is a cluster? Wait, no—wait, the first option: "All of the plants that are in one particular room are easily accessible. So, the botanist selects the 72 plants in this particular room." No, that's convenience. Wait, the second option: "The botanist forms groups of 8 plants based on the heights of the plants. Then, he randomly chooses 9 groups and selects all of the plants in these groups." Wait, no, the third option (with the blue dot) is "The botanist takes a list of the plants and selects every 3rd plant until 72 plants are selected." That's systematic sampling. Wait, the question is "Which of the following best describes a cluster sample of plants?" Cluster sampling: population divided into clusters (usually geographically or into groups), then some clusters are randomly selected, and all members of those clusters are sampled. Let's re - read:

Option 1: Selects all plants in one room (convenience, as room is accessible).

Option 2: Forms groups of 8 plants (maybe strata by height? No, cluster would be natural groups like rooms, but here groups by height, then selects 9 groups and all plants in them. Wait, maybe that's cluster. Wait, the blue dot is on the third option, but that's systematic (every 3rd). Wait, maybe I misread. Let's check again.

Wait, the first option: "All of the plants that are in one particular room are easily accessible. So, the botanist selects the 72 plants in this particular room." - convenience sampling.

Second option: "The botanist forms groups of 8 plants based on the heights of the plants. Then, he randomly chooses 9 groups and selects all of the plants in these groups." - If the groups are clusters (even if formed by height, but cluster sampling can have clusters formed in various ways, but usually natural clusters. However, stratified sampling is by strata (homogeneous within), cluster is heterogeneous within. But maybe this is cluster: selecting groups (clusters) and all in them.

Third option: "The botanist takes a list of the plants and selects every 3rd plant until 72 plants are selected." - systematic sampling.

So the correct cluster sample would be the second option (but the blue dot is on the third, maybe the image's blue dot is a distractor). Wait, the question is to identify cluster. Cluster sampling: divide into clusters, random sample of clusters, sample all in cluster. So the second option: forms groups (clusters), randomly chooses 9, selects all in them. So that's cluster.

Stratified sampling involves dividing the population into strata (groups with similar characteristics), then taking a sample from each stratum.

• Option 1: "The analyst forms 6 groups of customers based on the customers' mortgage amounts. Then, she selects 13 customers at random from each group." - This is stratified sampling, as we divide by mortgage amounts (strata) and sample from each.

• Option 2: "The analyst spends a day calling mortgage customers and selects the first 78 customers who answer because these customers are easily accessible." - convenience sampling.

• Option 3: "The analyst forms groups of 13 customers based on the cities the customers live in. Then, she selects all of the customers in 6 randomly chosen groups." - cluster sampling.

So the correct option for stratified is the first one (with the blue dot, likely the first option in the list).

Simple random sampling (SRS) with a computer program where every set of 90 seats is equally likely to be drawn is SRS.

• Option 1: "The supervisor forms 5 groups of seats based on the dates the seats were last replaced. Then, she selects 18 seats at random from each group." - stratified sampling (groups as strata, sample from each).

• Option 2: "The supervisor uses a computer program to draw 90 seats at random and selects these seats. Every set of 90 seats is equally likely to be drawn by the computer program." - simple random sampling.

• Option 3: "The supervisor takes a list of the seats and selects every 5th seat until 90 seats are selected." - systematic sampling.

So the correct option is the second one (with the blue dot, likely the second option in the list).

Answer:

The option "The botanist forms groups of 8 plants based on the heights of the plants. Then, he randomly chooses 9 groups and selects all of the plants in these groups." (assuming this is one of the options, likely the second one in the list)

Part (b)