Another Statistics Problem.?

A study was conducted in order to estimate μ, 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 σ = 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.

Another Statistics Problem.?
well my first guess was ....


The 95% confidence z-score is 1.65


so you want 8.5 hours +/- (1.65 * 3.6)


however that's not among the answers, so now I think


maybe what needs to be done is like this ...





have to be 97.5% sure it's not greater than 8.5 + delta,


and 97.5% sure it's not less than 8.5 + delta (it helps that all five answers have 8.5 in the middle of the two ends).


The z score for the 97.5% level is even bigger though, of course - 1.96 -





The biggest interval you have in your choices is (e)





9.7 - 8.5 = 1.2


1.2 / 3.6 = 0.3333 is the z-score





Am I going wrong by forgetting to square the standard deviation maybe to get the variance! Maybe that's how these things are done? I swore it was done usually in standard deviations though.





Tell me when you find it out.