document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=264825>Question 264825</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Could you please give me an idea on how to work this problem, I am so sketchy on where to start and what to do. Thank you. \r<BR>\n" );
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document.write( "A sample of 35 golfers showed that their average score on a particular golf course was 80 with a standard deviation of 6.  <BR>\n" );
document.write( "Answer each of the following (show all work):<BR>\n" );
document.write( "(A) Find the 95% confidence interval of the mean score for all 35 golfers.<BR>\n" );
document.write( "(B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 50 golfers instead of a sample of 35.<BR>\n" );
document.write( "(C) Which confidence interval is smaller and why? <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 #194913 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=194913\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A sample of 35 golfers showed that their average score on a particular golf course was 80 with a standard deviation of 6. <BR>\n" );
document.write( "Answer each of the following (show all work):<BR>\n" );
document.write( "(A) Find the 95% confidence interval of the mean score for all 35 golfers.<BR>\n" );
document.write( "The sample mean = xbar = 80<BR>\n" );
document.write( "The standard error se = invNorm(0.025)*s/sqrt(n) = 1.96*6/sqrt(35) = 1.9878<BR>\n" );
document.write( "95% CI: xbar-se < u < xbar+se\r<BR>\n" );
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document.write( "95% CI: 80-1.9878 < u < 80+1.9878<BR>\n" );
document.write( "95% CI: 78.0122 < u < 81.9878<BR>\n" );
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document.write( "(B) Find the 95% confidence interval of the mean score for all golfers if this is a sample of 50 golfers instead of a sample of 35.<BR>\n" );
document.write( "xbar = 80<BR>\n" );
document.write( "standard error = 1.96*6/sqrt(50) = 1.6631<BR>\n" );
document.write( "95% CI: 78.337 < u < 81.6631<BR>\n" );
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document.write( "(C) Which confidence interval is smaller and why?<BR>\n" );
document.write( "The last one which has a larger sample size.<BR>\n" );
document.write( "Why?  As sample size increases the standard error decreases<BR>\n" );
document.write( "because sqrt(n) is in the denominator.  As n get larger<BR>\n" );
document.write( "the s/sqrt(n) gets smaller so the CI interval gets smaller;<BR>\n" );
document.write( "the CI interval is always twice the standard error in width.<BR>\n" );
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document.write( "If any of the above is not clear, please say so.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. <BR>\n" );
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