A student wants to survey the sophomore class of 200 students about whether the school should require uniforms. A random sample of 18 sophomores is surveyed and asked whether they support the school adopting uniforms, and three students said yes. The student wants to construct a 95% confidence interval for the proportion of sophomores who favor the adoption of uniforms. Are the conditions for inference met?

The sample was selected randomly, and 18 is less than 10% of the 200 sophomores (10% is 20), so those conditions are met. For a confidence interval for a proportion, the Large Counts Condition requires at least 10 expected successes and 10 expected failures in the sample. Here there are 3 students who said yes and 15 who said no, so the condition is not met; the correct choice is “No, the Large Counts Condition is not met.”

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