Practice Problems: Confidence Intervals - Answer

A sample of Alzheimer's patients are tested to assess the amount of time in stage IV sleep. It has been hypothesized that individuals sufferering from Alzheimer's Disease may spend less time per night in the deeper stages of sleep. Number of minutes spent is Stage IV sleep is recorded for sixty-one patients. The sample produced a mean of 48 minutes (S=14 minutes) of stage IV sleep over a 24 hour period of time. Compute a 95 percent confidence interval for this data. What does this information tell you about a particular individual's (an Alzheimer's patient) stage IV sleep?

The standard error of the mean is 1.807392228.

t=2.000

Confidence Interval at 95 percent: 43.5 < population mean < 52.5

We are 95 percent sure that the population mean for the number of hours an Alzheimer's patient will spend in stage IV sleep in a 24 period of time is somewhere between 44.4 minutes and 51.6 minutes. There is a 5 percent chance than the population mean for stage IV sleep in Alzheimer's patients is less than 44.4 minutes or more than 51.6 minutes.

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