document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=128116>Question 128116</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Problem Two:                                   \r<BR>\n" );
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document.write( "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.\r<BR>\n" );
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document.write( "(1)     Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.\r<BR>\n" );
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document.write( "(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?\r<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #93830 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=93830\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A survey of 100 randomly selected undergraduate students shows that 33% prefer to study in their rooms. <BR>\n" );
document.write( "(1) Construct a 95% confidence interval for the proportion of students who prefer to study in their rooms.<BR>\n" );
document.write( "E = z*sqrt(pq/n) <BR>\n" );
document.write( "E = 1.96[sqrt(0.33)(0.67)/(100)] = 1.96*0.0470= 0.0922<BR>\n" );
document.write( "C.I. = (0.33-0.0922,0.33+0.0922) etc.<BR>\n" );
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document.write( "(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? <BR>\n" );
document.write( "To be 95% confident they should provide at least 42.22% of the students<BR>\n" );
document.write( "with larger rooms.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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