SOLUTION: Problem Two: In designing a new dormitory, a progressive university wishes to determine where students prefer to study in order to provide app

Question 128116: Problem Two:
In designing a new dormitory, a progressive university wishes to determine where students prefer to study in order to provide appropriate space. A survey of 100 randomly selected undergraduate students shows that 33% prefer to study in their rooms.
(1) Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.
(2) If university has the option of making various sized rooms, what proportion of the rooms should be made larger to accommodate those who wish to study in their rooms?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A survey of 100 randomly selected undergraduate students shows that 33% prefer to study in their rooms.
(1) Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.
E = z*sqrt(pq/n)
E = 1.96[sqrt(0.33)(0.67)/(100)] = 1.96*0.0470= 0.0922
C.I. = (0.33-0.0922,0.33+0.0922) etc.
=================
(2) If university has the option of making various sized rooms, what proportion of the rooms should be made larger to accommodate those who wish to study in their rooms?
To be 95% confident they should provide at least 42.22% of the students
with larger rooms.
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Cheers,
Stan H.
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