Psychology: Sleep Many studies in the past have reported connections between sleep and cognitive functions. One such study analyzed how the amount of sleep a student gets might affect their exam score.

Students were divided into three randomized groups categorized by the amount of sleep and then were all asked to take the same math exam. Let x1, x2, and x3 be random variables representing a person’s test score through x1 (628 hours of sleep), x2 (325 hours of sleep), and x3 (2 or less hours of sleep). The test scores are reported in percentages.

Variable Sample Size Mean x¯

Standard Deviation, s Population Mean x1 15 89.3 3.01 m1 x2 15 85.6 3.62 m2 x3 15 81.4 3.74 m3

(a) Find an 85% confidence interval for m1 2m2.

(b) Find an 85% confidence interval for m1 2m3.

(c) Find an 85% confidence interval for m2 2m3.

(d) Interpretation Comment on the meaning of each confidence interval found in parts (a), (b), and

(c). At the 85% confidence level, what can you say about the average differences in test grades between students who got 628 hours of sleep and those who got 325 hours of sleep? between students who got 628 hours of sleep and those who got 2 or less hours of sleep? between students who got 325 hours of sleep and those who got 2 or less hours of sleep?

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