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Difficulty: MediumStatistical Sampling and Studies

An agricultural researcher wants to evaluate the effectiveness of a new organic fertilizer. The researcher selects a random sample of 8080 tomato plants of a specific variety from a greenhouse containing 1,2001,200 tomato plants of this variety. The researcher randomly assigns 4040 of the selected plants to receive the organic fertilizer and the remaining 4040 plants to receive a standard chemical fertilizer. At the end of the study, the plants that received the organic fertilizer produced a significantly higher average yield of tomatoes than the plants that received the standard chemical fertilizer. Based on this information, which of the following is the most appropriate conclusion?

  1. A
    The organic fertilizer causes a higher average yield of tomatoes than the standard chemical fertilizer for all tomato plants of this variety.
  2. The organic fertilizer causes a higher average yield of tomatoes than the standard chemical fertilizer for the 1,2001,200 tomato plants of this variety in the greenhouse.Answer
  3. C
    The organic fertilizer causes a higher average yield of tomatoes than the standard chemical fertilizer for all plants in the greenhouse.
  4. D
    There is an association between the organic fertilizer and a higher average yield of tomatoes, but it cannot be concluded that the fertilizer caused the higher yield for the plants in the greenhouse.

Answer

The organic fertilizer causes a higher average yield of tomatoes than the standard chemical fertilizer for the 1,2001,200 tomato plants of this variety in the greenhouse.
The study design includes both random sampling from a defined population (the 1,2001,200 tomato plants of this variety in the greenhouse) and random assignment of treatments (the fertilizers). Random assignment allows the researcher to conclude that the organic fertilizer caused the difference in yield, while random sampling allows this causal conclusion to be generalized to the entire population of 1,2001,200 tomato plants.

Step-by-Step Solution

1
Determine if a cause-and-effect relationship can be established.
A cause-and-effect relationship can be established because the treatments (organic fertilizer vs. standard chemical fertilizer) were randomly assigned to the selected plants.
Random assignment of treatments minimizes the influence of confounding variables, allowing the researcher to conclude that differences in the outcome are caused by the treatments.
2
Identify the population to which the causal conclusion can be generalized.
The causal conclusion can be generalized only to the 1,2001,200 tomato plants of this specific variety in this greenhouse.
The sample of 8080 plants was randomly selected from this specific population of 1,2001,200 plants in the greenhouse. Generalizing to all tomato plants of this variety everywhere is not valid because the sample may not represent plants in other environments. Generalizing to other species of plants in the greenhouse is not valid because only one specific variety of tomato plant was studied.

Key Concept

Generalizability and causal inference in statistical studies.
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Topics

Statistical Sampling and Studies

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