document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866660>Question 866660</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose we want a 90% confidence interval for the average amount of time (in minutes) spent per week on homework by the students in a large introductory statistics course at a large university.  The interval is to have a margin of error of 2 minutes, and the amount spent has a Normal distribution with a standard deviation = 30 minutes. \r<BR>\n" );
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document.write( "The number of observations required is \r<BR>\n" );
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document.write( "25\r<BR>\n" );
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document.write( "30\r<BR>\n" );
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document.write( "608\r<BR>\n" );
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document.write( "609<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 #522417 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=522417\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use this <a  rel=nofollow HREF=\"http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg\">table</a> to find the critical value to be z = 1.645 (look in the row that starts with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=infinity ALIGN=MIDDLE  ALT=\"infinity\"   DISABLED_style= \"max-width:90%; height:auto;\" >, look above the 90%)\r<BR>\n" );
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document.write( "So we know the following info\r<BR>\n" );
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document.write( "ME = 2 (given margin of error)<BR>\n" );
document.write( "s = 30 (given standard deviation)<BR>\n" );
document.write( "z = 1.645 (found using the table given above)\r<BR>\n" );
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document.write( "Margin of Error (ME)\r<BR>\n" );
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document.write( "ME = z*s/sqrt(n)\r<BR>\n" );
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document.write( "2 = 1.645*30/sqrt(n)\r<BR>\n" );
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document.write( "2 = 49.35/sqrt(n)\r<BR>\n" );
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document.write( "2*sqrt(n) = 49.35\r<BR>\n" );
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document.write( "sqrt(n) = 49.35/2\r<BR>\n" );
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document.write( "sqrt(n) = 24.675\r<BR>\n" );
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document.write( "n = (24.675)^2\r<BR>\n" );
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document.write( "n = 608.855625\r<BR>\n" );
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document.write( "n = 609  <font color=\"blue\">round UP to the nearest whole number</font>\r<BR>\n" );
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document.write( "Why do we round up? Well if we round down to 608, then we will have a margin of error (ME) larger than 2. We round up to clear this hurdle (since larger n leads to smaller ME). This happens whenever you get a decimal result for these type of problems.\r<BR>\n" );
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document.write( "So you need a sample size of at least <font color=\"red\">609</font> students to make sure the margin of error (ME) is 2 or less.<BR>\n" );
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