Samples of aircrew on long haul schedules are tested to asse

Samples of aircrew on long haul schedules are tested to assess the amount of time they spend in stage IV sleep. It has been hypothesized that individuals suffering from tiredness due to long haul work may spend less time per night in the deeper stages of sleep. The number of minutes spent in Stage IV sleep is recorded for sixty-one patients. The sample produced a mean of 48 minutes (sd=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 stage IV sleep?

Solution

Given a=0.05, Z(0.025) = 1.96 (from standard normal table)

So 95 percent confidence interval for this data is

xbar +/- Z*s/vn

-->48 +/- 1.96*14/sqrt(61)

--> (44.48667, 51.51333)

We have 95% confident that the population mean will be within this interval.