Question

the plants in your neighbors garden are in the repeated order of lilacs, sunflowers, dandelions, and roses. you decide to take a systematic sample using an interval of 4 plants, starting from plant. using your systematic sample, you estimate that of the 32 plants in her garden, 32 are dandelions. how accurate is your estimate? explain

choose the correct answer below.

a. the estimate is not accurate. the pattern in the plants does not introduce any bias in the sample, so it is not representative of the population.

b. the estimate is not accurate. the pattern in the plants introduces a bias in the sample, so it is not representative of the population.

c. the estimate should be fairly accurate. the pattern in the plants does not introduce any bias in the sample, so it should be representative of the population.

d. the estimate should be fairly accurate. the pattern in the plants does not introduce any bias in the sample, so it is not representative of the population.

Explanation:

Systematic sampling works well when there is no underlying pattern in the population. Here, the plants are in a repeated order (lilacs, sunflowers, dandelions, roses). If we start the systematic sample from plant \(1\) (lilac) and use an interval of \(4\), we will always get lilacs (since \(1 + 4n\) will cycle through the first plant of the repeating pattern). But we estimated the number of dandelions. The pattern in the plants (the fixed order of plant types) introduces a bias. A biased sample is not representative of the population.

Answer:

B. The estimate is not accurate. The pattern in the plants introduces a bias in the sample, so it is not representative of the population.