document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=868431>Question 868431</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Although male polar bears weigh only about one pound at birth, the mean weight of a random sample of 10 adult male polar bears is 1200 pounds with a standard deviation of 100 pounds. Construct and interpret a 98% confidence interval for the mean weight of all adult male polar bears. Assume that the population is evenly distributed. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #523872 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=523872\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Use <a  rel=nofollow HREF=\"http://3.bp.blogspot.com/_5u1UHojRiJk/TEdJJc6of2I/AAAAAAAAAIE/Ai0MW5VgIhg/s1600/t-table.jpg\">a table</a> to find that the critical value is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=t=2.821 ALIGN=MIDDLE  ALT=\"t=2.821\"   DISABLED_style= \"max-width:90%; height:auto;\" >. The degrees of freedom are <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=df+=+n-1+=+10-1+=+9 ALIGN=MIDDLE  ALT=\"df+=+n-1+=+10-1+=+9\"   DISABLED_style= \"max-width:90%; height:auto;\" >. Look in the row that starts with <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=9 ALIGN=MIDDLE  ALT=\"9\"   DISABLED_style= \"max-width:90%; height:auto;\" > and look above the 98%. The value you'll see in this spot is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.821 ALIGN=MIDDLE  ALT=\"2.821\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So we're given\r<BR>\n" );
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document.write( "xbar = 1200 (sample mean)<BR>\n" );
document.write( "t = 2.821 (see above)<BR>\n" );
document.write( "s = 100 (sample standard deviation)<BR>\n" );
document.write( "n = 10 (sample size)\r<BR>\n" );
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document.write( "Now compute the lower bound (L) and the upper bound (U) of the confidence interval.\r<BR>\n" );
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document.write( "Lower Bound:\r<BR>\n" );
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document.write( "L = xbar - t*s/sqrt(n)<BR>\n" );
document.write( "L = 1200 - 2.821*100/sqrt(10)<BR>\n" );
document.write( "L = 1,110.79214720666\r<BR>\n" );
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document.write( "Upper Bound:\r<BR>\n" );
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document.write( "U = xbar + t*s/sqrt(n)<BR>\n" );
document.write( "U = 1200 + 2.821*100/sqrt(10)<BR>\n" );
document.write( "U = 1,289.20785279334\r<BR>\n" );
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document.write( "The 98% confidence interval is approximately <font color=\"red\">(1110.79214720666,   1289.20785279334)</font>\r<BR>\n" );
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document.write( "So if we construct 100 confidence intervals, then about 98 of them will contain the true population mean. </SPAN>\n" );
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