document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981707>Question 981707</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A psychologist is interested in knowing whether adults who were bullied as children differ from the general population in terms of their empathy for others. On a questionnaire designed to measure empathy, the mean score for the general population is 48.96. Random sampling of 25 scores obtained from individuals who were bullied yielded a mean of 54.04 and a standard deviation of 11.49. (Use these numbers only for this question!)\r<BR>\n" );
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document.write( "Calculate the 99% confidence interval.<BR>\n" );
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document.write( "As you know, two values will be required to complete the following equation:<BR>\n" );
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document.write( "_________ &#8804; µ &#8804; __________\r<BR>\n" );
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document.write( "For this question, what is the value that is below or less than µ?<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 #602661 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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/cgi-bin/show-face.mpl?user=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=602661\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> 1) Calculate the Margin of Error(ME)<BR>\n" );
document.write( "ME = Z(alpha/2) * std.dev. / square root(n) where<BR>\n" );
document.write( "Z(alpha/2) is the confidence coefficient = (1 - 0.99) / 2 = 0.005, now consult  z table to find the corresponding value that goes with probability 0.005<BR>\n" );
document.write( "z-value = -2.58<BR>\n" );
document.write( "note that we ignore the - sign in the z-value<BR>\n" );
document.write( "ME = 2.58 * 11.49 / square root(25) = 5.92884<BR>\n" );
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document.write( "2) confidence interval(CI) = sample mean + or minus ME<BR>\n" );
document.write( "CI = 54.04 + or - 5.92884, therefore<BR>\n" );
document.write( "CI = 48.11116 < or = u < or = 59.96884<BR>\n" );
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document.write( "3) The value that is below or less than µ is 48.11116\r<BR>\n" );
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