AP Statistics 1.12: Sampling Bias

Identify potential sampling bias by tracing volunteers, missing groups, nonrespondents, and response wording to distorted estimates.

[Maximum number: 4]

Aphids are tiny insects that feed on plants such as cabbage plants. A farmer wants to reduce the

number of aphids in a cabbage field. A river is located 100 meters south of the cabbage field.

The farmer divides the field into 25 regions of equal size, as shown in the diagram. Each region

has approximately the same number of cabbage plants.

Farmer's House and Cabbage Field

The farmer would like to estimate the proportion of cabbage plants in the field that are affected

by aphids and believes that the extent of aphid damage is greater for the regions in the cabbage

field closer to the river. To obtain the estimate, the farmer is considering three sampling

methods.

- Sampling method I: Select region 3, which is closest to the farmer's house and farthest

from the river. Examine every cabbage plant in the region for aphid damage.

- Sampling method II: Randomly select one row (A, B, C, D, or E). For every region in the

selected row, examine every cabbage plant for aphid damage.

- Sampling method III: Randomly select one region from each of rows A, B, C, D, and E. For

each selected region, examine every cabbage plant for aphid damage.

(a)

Explain whether sampling method I is an appropriate sampling method for the farmer to use

to estimate the proportion of cabbage plants in the field that are damaged by aphids.

(b)

Using sampling method II, the farmer randomly selected row E and examined every cabbage

plant in row E. If the farmer's belief is correct, determine whether the selection of row E is

likely to provide an overestimate or an underestimate of the proportion of cabbage plants in

the field that are damaged by aphids. Justify your answer.

	Model Solution	Scoring
B	The selection of row E is likely to provide an overestimate of the proportion of all cabbage plants in the field that are damaged by aphids. If the farmer's belief that the extent of aphid damage is greater for the regions in the cabbage field closer to the river is correct, then row E, which is the row of regions located closest to the river, is likely to have a greater proportion of cabbage plants damaged by aphids than regions farther from the river.	Essentially correct (E) if the response satisfies the following three components: 1. Indicates that the selection of row E is likely to produce an overestimate 2. Provides a justification that is based on the location of row E as the row located closest to the river 3. Links the location to why row E is likely to produce an overestimate (e.g., by referring to the farmer's belief that the extent of aphid damage is greater for the regions in the cabbage field closer to the river) Partially correct (P) if the response satisfies only two of the three components required for E. Incorrect (I) if the response does not meet the criteria for E or P.

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