Should the choices made by 100 participants in a survey about Product X be said to proportionately represent the preferences...

Understanding the Question

We need to determine whether a 100-person survey about Product X can be said to "proportionately represent" the entire population's preferences. This is a yes/no question: Can we definitively answer either YES (it does proportionately represent) or NO (it doesn't)?

What "Sufficient" Means Here

To have sufficient information, we need to be able to give a definitive YES or NO answer about whether this survey proportionately represents the population.

Key Considerations for Representative Surveys

For a survey to proportionately represent a population, we typically need to know:

• Selection method: How were participants chosen? (random sampling vs. convenience sampling)
• Population characteristics: Size, demographics, and relevant attributes
• Sample adequacy: Is 100 people enough for this specific population?
• Potential biases: Any systematic exclusions or overrepresentations?

Without this information, we cannot determine representativeness.

Analyzing Statement 1

Statement 1 tells us: In the survey of 100 participants, 70% said they preferred Product X.

This gives us the survey result, but notice what's missing:

• How were these 100 people selected?
• Was this a random sample or were certain groups targeted?
• What's the total population size and composition?
• Could there be selection bias (e.g., surveying only Product X users)?

The 70% preference rate is just an outcome—it tells us nothing about whether this outcome proportionately represents the population. For example:

• A biased sample of Product X enthusiasts could show 70% preference but not represent the general population
• A perfectly representative random sample could also show 70% preference

Without methodology information, we cannot answer YES or NO definitively.

[STOP - NOT Sufficient!]

Statement 1 is NOT sufficient.

This eliminates choices A and D.

Analyzing Statement 2

Now let's forget Statement 1 completely and analyze Statement 2 independently.

Statement 2 tells us: While the survey provided valuable insights into Product X, the small sample may not be representative of the entire population's preferences.

Let's parse this statement carefully. The key phrase is "may not be" representative. This is crucial because:

• "May not be" expresses uncertainty, not a definitive conclusion
• It suggests a possibility that the sample isn't representative
• It does NOT definitively state that the sample IS or ISN'T representative

This ambiguous language prevents us from answering:

• YES (it definitely is proportionately representative), or
• NO (it definitely is not proportionately representative)

The statement raises a concern about sample size but doesn't resolve whether the survey actually represents the population or not.

[STOP - NOT Sufficient!]

Statement 2 is NOT sufficient.

This eliminates choice B (we already eliminated D).

Combining Statements

Using both statements together, we have:

• From Statement 1: The survey result shows 70% preference rate
• From Statement 2: A concern that the sample "may not be" representative due to its small size

Even combining both pieces of information, we still face the fundamental problem: ambiguity remains. Consider what we still don't know:

• The actual sampling methodology used
• Whether 100 is truly inadequate for this specific population
• The degree of confidence in the survey results
• Whether the "may not be" concern is valid or just cautionary

The phrase "may not be representative" in Statement 2 continues to prevent any definitive conclusion. We cannot say with certainty:

• YES, the survey proportionately represents the population, or
• NO, the survey does not proportionately represent the population

[STOP - NOT Sufficient!]

Statements 1 and 2 together are NOT sufficient.

This eliminates choice C (we already eliminated A, B, and D).

The Answer: E

Neither statement alone nor both together provide enough information to definitively answer whether the survey proportionately represents the population's preferences. The ambiguous language in Statement 2 ("may not be") combined with the lack of methodology information prevents any definitive YES or NO conclusion.

Answer Choice E: "The statements together are not sufficient."