document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=662733>Question 662733</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A sample of 106 golfers showed that their average score on a particular golf course was 87.98 with a standard deviation of 5.39.<BR>\n" );
document.write( "Answer each of the following (SHOW ALL WORK and state the FINAL answer to at least TWO Decimal places):\r<BR>\n" );
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document.write( "(A) Find the 90% confidence interval of the mean score for all 106 golfers.\r<BR>\n" );
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document.write( "(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 106.\r<BR>\n" );
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document.write( "(C) Which confidence interval is larger and why?\r<BR>\n" );
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document.write( "Thank you for your help!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #412460 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=412460\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 106 golfers showed that their average score on a particular golf course was 87.98 with a standard deviation of 5.39.<BR>\n" );
document.write( "Answer each of the following (SHOW ALL WORK and state the FINAL answer to at least TWO Decimal places): <BR>\n" );
document.write( "(A) Find the 90% confidence interval of the mean score for all 106 golfers.<BR>\n" );
document.write( "x-bar = 87.98<BR>\n" );
document.write( "ME = 1.645*5.39/sqrt(106) = 0.8612<BR>\n" );
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document.write( "90% CI: 87.98-0.8612 < u < 87.98+0.8612<BR>\n" );
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document.write( "(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 130 golfers instead of a sample of 106.<BR>\n" );
document.write( "new ME = 1.645*5.39/sqrt(130) = 0.7776<BR>\n" );
document.write( "90% CI: 87.98-0.7776 < u < 87.98+0.7776<BR>\n" );
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document.write( "(C) Which confidence interval is larger and why?<BR>\n" );
document.write( "The 1st is larger because the sample size is smaller.<BR>\n" );
document.write( "Note 2 things:<BR>\n" );
document.write( "1st: The CI is ALWAYS 2*ME in width<BR>\n" );
document.write( "2nd: Since ME and sqrt(n) are indirectly related, ME gets<BR>\n" );
document.write( "smaller when n gets larger.<BR>\n" );
document.write( "That makes sense because having a larger sample means you<BR>\n" );
document.write( "have more information; so the confidence interval can be tighter.<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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