A study was conducted in order to estimate the mean number

A study was conducted in order to estimate ?, the mean number of weekly hours that U.S. adults use computers at home. Suppose a random sample of 81 U.S. adults gives a mean weekly computer usage time of 8.5 hours and that from prior studies, the population standard deviation is assumed to be ? = 3.6 hours.

We are 95% confident that the mean number of weekly hours that U.S. adults use computers at home is:

A between 8.1 and 8.9.

B between 7.8 and 9.2.

C between 7.7 and 9.3.

D between 7.5 and 9.5.

E between 7.3 and 9.7.

Solution

Given a=1-0.95=0.05, Z(0.025) = 1.96 (from standard normal table)

So the lower bound is

xbar - Z*s/vn =8.5 -1.96*3.6/sqrt(81) =7.716

So the upper bound is

xbar + Z*s/vn =8.5 +1.96*3.6/sqrt(81)=9.284

Answer: C between 7.7 and 9.3.