document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=165502>Question 165502</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help with my homework question on Interval Estimations.  The book is Statistics for Business and Economics. A sample survey of 54 discount brokers showed that the mean price charged for a trade of 100 shares at $50 per share was $33.77.  The survey is conducted annually.  With the historical data available, assume a known population standard deviation of $15.\r<BR>\n" );
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document.write( "a.  Using the sample data, what is the margin of error associated with a 95% confidence interval?\r<BR>\n" );
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document.write( "b.  Develop a 95% confidence interval for the mean price charged by discount brokers for a trade of 100 shares at $50 per share. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #122046 by </B><A HREF=/tutors/aboutme.mpl?userid=gonzo><B>gonzo(654)</B></A><img src=\"/images/stars/stars-11.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=gonzo><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=122046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> i don't have your book but i've done some research online and have come up with the following:<BR>\n" );
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document.write( "n = 54 = sample size.<BR>\n" );
document.write( "standard deviation of population is 15.<BR>\n" );
document.write( "you are looking for a confidence level of 95%<BR>\n" );
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document.write( "the formula for determining the margin of error associated with a 95% confidence interval looks very much like it is:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=E+=+Z+of+%28alpha%2F2%29+%2A+SD%2Fsqrt%28n%29 ALIGN=MIDDLE  ALT=\"E+=+Z+of+%28alpha%2F2%29+%2A+SD%2Fsqrt%28n%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "E is the margin of error you are looking for.<BR>\n" );
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document.write( "(alpha/2) is 1 - confidence level you are looking for divided by 2.  since the confidence level you are looking for is 95%, (alpha/2) is (1-.95)/2 = .05/2 = .025.<BR>\n" );
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document.write( "Z of (.025) would be the value of Z where the right hand tail of the normal distribution begins.<BR>\n" );
document.write( ".025 of the area under the curve is to the right of that point.<BR>\n" );
document.write( "that equates to a Z value of 1.96 which means that you are 1.96 standard deviations to the right of the mean.<BR>\n" );
document.write( "in the standard Z table, the mean is 0 and the standard deviation is 1.<BR>\n" );
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document.write( "SD is the standard deviation of the population = 15.<BR>\n" );
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document.write( "n is the sample size = 54.<BR>\n" );
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document.write( "the formula becomes:<BR>\n" );
document.write( "E = 1.96 * (15/sqrt(54)<BR>\n" );
document.write( "This comes out to be:  4.000833247.<BR>\n" );
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document.write( "looks like your margin of error is +/- 4.000833247<BR>\n" );
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document.write( "the confidence interval is twice the margin of error.<BR>\n" );
document.write( "if your mean is 33.77, then your margin of error is +/- 4.000833247 from that.<BR>\n" );
document.write( "that makes your confidence interval from 29.77 to 37.77 at 95% confidence level.<BR>\n" );
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document.write( "that's what i think.  i'm reasonably sure this is correct.  check with others to make sure.<BR>\n" );
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