SAT-Style: Statistical Claims and Sampling

SAT Math · Axiom Academy

SAT-Style Statistical Claims & Sampling Evaluate whether study conclusions are justified Problem 1: Identifying Sampling Bias Study: A researcher surveyed 200 people exiting a gym to determine the average amount of exercise Americans get per week. Results showed Americans exercise an average of 5.5 hours per week. Question: Explain why this study's conclusion may be unreliable, and what bias is present. People who don't exercise at all Gym users are by definition more active than the general American population. The average from this biased sample (5.5 hours) is much higher than the true population average would be, because inactive people are completely excluded. A more valid approach would be: Randomly select people from the general population (not just gym users) Use a diverse mix including various age groups, income levels, and regions Ask about all forms of exercise, not just gym activity Problem 2: Observational Study vs. Causal Claims Study: Researchers followed 500 adults for 5 years, recording how much coffee they drank and monitoring their health. The study found that people who drank 3+ cups of coffee per day had a 20% lower risk of heart disease. Question: Can we conclude that coffee prevents heart disease? This is an observational study . Researchers observed existing groups (heavy coffee drinkers vs. light drinkers) but didn't control or assign treatments. Exercise habits (coffee drinkers might be more active) Diet quality (coffee drinkers might eat healthier)

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