Does sleep improve mental performance? Are creativity and problem solving linked to adequate sleep? This question was the subject of research conducted by German scientists at the University of Lübeck ( Nature,Jan. 22, 2004). One hundred volunteers were divided into two equal-sized groups. Each volunteer took a math test that involved transforming strings of eight digits into a new string that fit a set of given rules, as well as a third, hidden rule. Prior to taking the test, one group received eight hours of sleep, while the other group stayed awake all night. The scientists monitored the volunteers to determine whether and when they figured out the third rule. Of the volunteers who slept, 39 discovered the third rule; of the volunteers who stayed awake all night, 15 discovered the third rule. From the study results, what can you infer about the proportions of volunteers in the two groups who discover the third rule? Support your answer with a 90% confidence interval.
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