document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1204517>Question 1204517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Construct the indicated confidence interval for the population mean μ using the​ t-distribution. Assume the population is normally distributed.<BR>\n" );
document.write( "c=0.90​,  x=13.5​,  s=0.77​,  n=15<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 #840832 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20850)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=840832\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <BR>\n" );
document.write( "The formula for estimation is:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+M+%2B-+t%28s%5BM%5D%29 ALIGN=MIDDLE  ALT=\"mu+=+M+%2B-+t%28s%5BM%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "where:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M ALIGN=MIDDLE  ALT=\"M\"   DISABLED_style= \"max-width:90%; height:auto;\" > = sample mean<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t ALIGN=MIDDLE  ALT=\"t\"   DISABLED_style= \"max-width:90%; height:auto;\" > = t statistic determined by confidence level<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s%5BM+%5D ALIGN=MIDDLE  ALT=\"s%5BM+%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >= standard error = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=sqrt%28s%5E2%2Fn%29 ALIGN=MIDDLE  ALT=\"sqrt%28s%5E2%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "given\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=M=+13.5 ALIGN=MIDDLE  ALT=\"M=+13.5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=15 ALIGN=MIDDLE  ALT=\"n=15\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=s=0.77 ALIGN=MIDDLE  ALT=\"s=0.77\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=c=+0.90 ALIGN=MIDDLE  ALT=\"c=+0.90\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "A <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" >% Confidence Interval will have the same critical values (rejection regions) as a two-tailed <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z ALIGN=MIDDLE  ALT=\"z\"   DISABLED_style= \"max-width:90%; height:auto;\" > test with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=alpha+=+.10 ALIGN=MIDDLE  ALT=\"alpha+=+.10\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF=\"https://ibb.co/dr7sCGz\"><IMG STYLE=\"max-width:80%;\" src=\"https://i.ibb.co/dr7sCGz/zc-CI90-Table-1024x426.jpg\" alt=\"zc-CI90-Table-1024x426\" border=\"0\"></a>\r<BR>\n" );
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document.write( "so, z-score for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" >% confidence interval is ±<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1.6445 ALIGN=MIDDLE  ALT=\"1.6445\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+M+%2B-+t%28s%5BM%5D%29 ALIGN=MIDDLE  ALT=\"mu+=+M+%2B-+t%28s%5BM%5D%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+M+%2B-+t%28sqrt%28s%5E2%2Fn%29%29 ALIGN=MIDDLE  ALT=\"mu+=+M+%2B-+t%28sqrt%28s%5E2%2Fn%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=13.5+%2B-+1.6445sqrt%280.77%5E2%2F15%29 ALIGN=MIDDLE  ALT=\"mu+=13.5+%2B-+1.6445sqrt%280.77%5E2%2F15%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu+=+13.5+%2B-+0.326948217125689 ALIGN=MIDDLE  ALT=\"mu+=+13.5+%2B-+0.326948217125689\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" >%  confidence interval is [<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.17 ALIGN=MIDDLE  ALT=\"13.17\"   DISABLED_style= \"max-width:90%; height:auto;\" >, <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.83 ALIGN=MIDDLE  ALT=\"13.83\"   DISABLED_style= \"max-width:90%; height:auto;\" >]\r<BR>\n" );
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document.write( "You can be <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=90 ALIGN=MIDDLE  ALT=\"90\"   DISABLED_style= \"max-width:90%; height:auto;\" >% confident that the population mean (<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu ALIGN=MIDDLE  ALT=\"mu\"   DISABLED_style= \"max-width:90%; height:auto;\" >) falls between <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.17 ALIGN=MIDDLE  ALT=\"13.17\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=13.83 ALIGN=MIDDLE  ALT=\"13.83\"   DISABLED_style= \"max-width:90%; height:auto;\" >.\r<BR>\n" );
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