document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=866626>Question 866626</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Here are the IQ test scores of 31 seventh-grade girls in a Midwest school district: <BR>\n" );
document.write( "114    100    104    89    102    91    114    114    103    105<BR>\n" );
document.write( "108    130    120   132   111   128   118     119    86      72<BR>\n" );
document.write( "111    103     74    112   107   103    98      96    112    112   93\r<BR>\n" );
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document.write( "These 31 girls are an SRS of all seventh-grade girls in the school district. <BR>\n" );
document.write( "Suppose that the standard deviation of IQ scores in this population is known to be &#963; = 15. We expect the distribution of IQ scores to be close to Normal. \r<BR>\n" );
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document.write( "Estimate the mean IQ score for all seventh-grade girls in the school district, using a 98% confidence interval.\r<BR>\n" );
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document.write( "Question 2 options:<BR>\n" );
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document.write( "105.84 to 132.00<BR>\n" );
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document.write( "72.00 to 132.00<BR>\n" );
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document.write( "100.56 to 111.12<BR>\n" );
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document.write( "99.57 to 112.11<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 #522398 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=522398\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First find the sample mean. You do so by adding up all the numbers and dividing by 31 (since there are 31 numbers). \r<BR>\n" );
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document.write( "Add up all the numbers to get 3281. Divide this by 31 to get 3281/31 = 105.8387\r<BR>\n" );
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document.write( "The sample mean is usually denoted xbar, so xbar = 105.8387 (this is approximate)\r<BR>\n" );
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document.write( "Now we turn to this <a  rel=nofollow HREF=\"http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg\">table</a>. 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;\" > and look above the 98%. The value you'll see in this spot is 2.326\r<BR>\n" );
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document.write( "The critical value is z = 2.326\r<BR>\n" );
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document.write( "This is the critical value for the 98% confidence interval.\r<BR>\n" );
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document.write( "To sum things up, we found the following\r<BR>\n" );
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document.write( "xbar = 105.8387 (sample mean)<BR>\n" );
document.write( "z = 2.326 (critical value for the 98% confidence interval)\r<BR>\n" );
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document.write( "values above are approximate\r<BR>\n" );
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document.write( "The values given to us were\r<BR>\n" );
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document.write( "n = 31 (sample size)<BR>\n" );
document.write( "&#963; = 15 (population standard deviation)\r<BR>\n" );
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document.write( "We can finally compute the lower bound L and the upper bound U of the confidence interval\r<BR>\n" );
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document.write( "L = xbar - z*&#963;/sqrt(n)<BR>\n" );
document.write( "L = 105.8387 - 2.326*15/sqrt(31)<BR>\n" );
document.write( "L = 99.57227<BR>\n" );
document.write( "L = 99.57  <font color=\"blue\">rounding to 2 decimal places</font>\r<BR>\n" );
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document.write( "U = xbar + z*&#963;/sqrt(n)<BR>\n" );
document.write( "U = 105.8387 + 2.326*15/sqrt(31)<BR>\n" );
document.write( "U = 112.1051<BR>\n" );
document.write( "U = 112.11  <font color=\"blue\">rounding to 2 decimal places</font>\r<BR>\n" );
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document.write( "The confidence interval [L,U] or (L,U) is approximately [99.57, 112.11] or (99.57, 112.11)\r<BR>\n" );
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document.write( "So the answer is <font color=\"red\">99.57 to 112.11</font> which is <font color=\"red\">choice D</font> </SPAN>\n" );
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