document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200393>Question 1200393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n=440 and X = 352, construct a 99% confidence interval.\r<BR>\n" );
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document.write( "Give your answers to three decimals\r<BR>\n" );
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document.write( " ______< p <_______ <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 #845045 by </B><A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><B>amarjeeth123(569)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=amarjeeth123><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=845045\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Mean confidence interval: [-43.167 , 43.167].<BR>\n" );
document.write( "Alternatively: 0 ± 43.167<BR>\n" );
document.write( "Margin of Error (MOE): 43.167.<BR>\n" );
document.write( "Standard Error (S.E): 16.686.\r<BR>\n" );
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document.write( "Since you use the sample standard deviation (S), the formula uses the t-distribution with n-1 degrees of freedom.\r<BR>\n" );
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document.write( "If you would calculate the confidence interval over an infinite number of samples with a sample size of 440, 99% (CL) of the calculated confidence intervals will contain the mean's true value, and 1% (α) of the calculated confidence intervals will not contain the mean's true value.\r<BR>\n" );
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document.write( "Calculation steps<BR>\n" );
document.write( "The mean confidence interval formula is:<BR>\n" );
document.write( "x̄ ± MOE<BR>\n" );
document.write( "x̄ ± T1-α/2(df) *	S<BR>\n" );
document.write( "√n\r<BR>\n" );
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document.write( "Calculate the degrees of freedom:<BR>\n" );
document.write( "df = n - 1 = 440 - 1 = 439\r<BR>\n" );
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document.write( "Calculate the significance level:<BR>\n" );
document.write( "α = 1 - CL = 1 - 0.99 = 0.01.\r<BR>\n" );
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document.write( "Calculate the probability (p):<BR>\n" );
document.write( "p= 1 - α/2 = 1 - 0.01/2 = 0.995.\r<BR>\n" );
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document.write( "If we don't know the population standard deviation we have to use the t-distribution only.\r<BR>\n" );
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document.write( "Calculate the t-score:<BR>\n" );
document.write( "T0.995(439) = 2.587<BR>\n" );
document.write( "x̄ ± T0.995(439) *	350<BR>\n" );
document.write( "√440<BR>\n" );
document.write( "0 ± 2.587 *	350<BR>\n" );
document.write( "√440<BR>\n" );
document.write( "0 ± 2.587 * 16.686<BR>\n" );
document.write( "0 ± 43.167\r<BR>\n" );
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document.write( "Since Tα/2 = -T1-α/2 , you may use Tα/2 instead of T1-α/2 </SPAN>\n" );
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