Near the end of a US cable news show, the host invited viewers to respond to a poll on the...

1. TRANSLATE the problem setup

• Given information:
  • Cable news show conducted online poll
  • Question: "Do you support the new federal policy discussed during the show?"
  • Results: 28% Yes, 70% No
  • Asked: Why results unlikely to represent US population sentiments

2. INFER what makes a poll representative

• For poll results to represent the entire US population, the sample must be representative
• A representative sample should be randomly selected from the target population
• Selection bias occurs when certain groups are over- or under-represented

3. CONSIDER ALL CASES by examining each answer choice

Choice A: "Percentages don't add up to 100%"

• \(28\% + 70\% = 98\%\) (very close to 100%)
• Missing 2% could be "undecided" or rounding
• This doesn't invalidate poll conclusions

Choice B: "Respondents were not a random sample"

• Respondents had to: have cable TV, watch this specific show, access the website, choose to respond
• This creates multiple layers of selection bias
• These people likely differ systematically from the general US population

Choice C: "Results weren't 50-50"

• No statistical requirement for balanced results
• Valid polls can show skewed results if sample is representative

Choice D: "Not enough response time"

• Time constraints might affect response rate but don't necessarily bias the sample composition

4. INFER the fundamental issue

• The core problem is sample representativeness, not mathematical calculations or response rates
• Multiple selection biases make this sample unrepresentative of all Americans

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Weak INFER skills: Students focus on superficial mathematical issues rather than fundamental sampling methodology

Students notice that \(28\% + 70\% = 98\%\) (not exactly 100%) and think this mathematical imperfection invalidates the poll. They miss the deeper issue that the sample itself is biased regardless of how the percentages calculate.

This may lead them to select Choice A (percentages don't add to 100%).

Second Most Common Error:

Missing conceptual knowledge about polling methodology: Students don't understand what makes a sample representative

Without understanding random sampling and selection bias, students might think that any large group of responses is automatically representative of the population. They focus on procedural issues like response time rather than who actually responded.

This may lead them to select Choice D (not enough time).

The Bottom Line:

This problem tests understanding of statistical sampling principles, not mathematical calculations. The key insight is recognizing that who responds matters more than how many respond or what the exact percentages are.