Suppose you want to know the average amount of sleep you get per
night. You record your elapsed sleep time over 74 nights. The mean
is 7.9 and standard deviation is 2.2. Find a 95% confidence
interval for your mean number of hours of sleep per night. Report
the answer accurate to four decimal places
Here we have n = 74, = 7.9, s = 2.2
Here sample size larger. So we use z interval.
The 95% confidence interval is given by,
( - E , + E )
Where,
We use sample standard deviation as estimate of population standard deviation.
c = 0.95,
Zc =
Hence the 95% confidence interval is,
= 0.5013
Hence the 95 % confidence interval is given by,
( 7.9 - 0.5013, 7.9 + 0.5013)
( 7.3987, 8.4013 )
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