A nutritionist wants to estimate the average daily calorie intake of adults in a certain city. A random sample of...

1. TRANSLATE the problem information

• Given information:
  • Sample of 195 adults surveyed
  • Sample mean daily calorie intake = 2,200 calories
  • Margin of error = 120 calories
• We need to find the most appropriate conclusion about the population mean

2. INFER what margin of error tells us

• Margin of error doesn't mean we're exactly 120 calories off
• Instead, it creates a range of plausible values for the true population mean
• The true average is likely somewhere within: [sample mean - margin of error, sample mean + margin of error]

3. Calculate the confidence interval

• Lower bound: \(2{,}200 - 120 = 2{,}080\) calories
• Upper bound: \(2{,}200 + 120 = 2{,}320\) calories
• Plausible range: \([2{,}080, 2{,}320]\) calories

4. INFER which answer choice matches our reasoning

• We're looking for a choice that acknowledges this range of plausibility
• Choice B states: "It is plausible that the average is between 2,080 and 2,320 calories"
• This exactly matches our calculated confidence interval

Answer: B

Why Students Usually Falter on This Problem

Most Common Error Path:

Conceptual confusion about margin of error: Students often misunderstand what "margin of error" means, thinking it represents the actual average rather than the uncertainty in the estimate.

This leads them to think "120 calories" is somehow the answer, causing them to select Choice A (120 calories is the average daily intake).

Second Most Common Error:

Weak INFER reasoning about statistical estimates: Students treat the sample mean as if it were the exact population mean, ignoring the uncertainty that margin of error represents.

They think "We estimated 2,200 calories, so that must be the true average," leading them to select Choice C (The average is 2,200 calories).

The Bottom Line:

This problem tests whether students understand that sample statistics are estimates with uncertainty, not exact values. The margin of error quantifies that uncertainty by creating a range of plausible values for the true population parameter.