In a study of the effect of a new teaching technique on students' achievement test scores, an important extraneous variable would be the students': A. hair color. C. IQ scores. B. athletic skills. D. sociability.

Let's analyze each option in detail: A. Hair color: This variable is very unlikely to have an impact on students' academic performance. B. Athletic skills: Although athletic skills could be indirectly related to academic performance (e.g., through discipline and focus), it is not as directly related to learning new teaching techniques as other variables. C. IQ scores: IQ scores are a measure of a student's cognitive abilities which could impact how well they learn or adapt to new teaching techniques. This variable is more directly related to academic achievement. D. Sociability: While sociability might impact a student's classroom experience, it also doesn't have as direct of a relationship with academic achievement as other variables.

Based on the analysis of the options, it's clear that: A. Hair color is not relevant to academic achievement. B. Athletic skills are indirectly related, but not as directly related to learning new teaching techniques as other variables. D. Sociability is also indirectly related to academic achievement but doesn't have as direct of a relationship as other variables. C. IQ scores are directly related to academic achievement because they measure a student's cognitive abilities which could impact how well they learn or adapt to new teaching techniques. Therefore, IQ scores are the most important extraneous variable in this study.

The correct answer is C. IQ scores.