It has been extensively demonstrated that adequate night sleep is crucial for co

Question

It has been extensively demonstrated that adequate night sleep is crucial for cognitive performance. To investigate whether first year USC students are getting adequate sleep the night before a final exam, 81 randomly selected first year USC students were asked to record their number of hours of sleep the night before their final exams. The mean number of hours of sleep among the 81 students was 6.2 with an SD of 1.5 hours. Construct a 95% CI for the mean number of hours first year USC students sleep the night before an exam. Explain the meaning of this CI (you are expected to explain what this confidence interval says about the parameter of interest)

Explanation / Answer

n = 81

mean = 6.2

SD = 1.5

SE of mean = 1.5 / sqrt(81) =0.17

Critical value (CV) at 95% confidence interval = 1.96

Upper confidence interval = mean + 1.96*0.17

                                                = 6.2 + 1.96*0.17

                                                = 6.53

Lower Confidence interval = 6.2 - 1.96*0.17 = 5.87

The adequate sleep is in the interval (5.87 , 6.53)

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