A 95% confidence interval for the true proportion of teenagers who have been to a professional sporting event is (0.289, 0.416). Is it reasonable to believe that more than 25% of teenagers have been to a professional sporting event?

The 95% confidence interval is from 0.289 to 0.416, and even its lower endpoint, 0.289, is greater than 0.25. Thus the entire interval lies above 25%, so it is reasonable to believe that more than 25% of teenagers have been to a professional sporting event. The correct choice is “Yes, because the entire interval is greater than 0.25.”

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