document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1201637>Question 1201637</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey, 11 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $43 and standard deviation of $15. Construct a confidence interval at a 95% confidence level.\r<BR>\n" );
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document.write( "Give your answers to one decimal place.<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 #836183 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=836183\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 11.<BR>\n" );
document.write( "sample mean is 43 dollars.<BR>\n" );
document.write( "standard deviation is 15 dollars.<BR>\n" );
document.write( "because you are looking for the mean of a sample of specified size, use the standard error rather than the standard deviation.<BR>\n" );
document.write( "standard error = standard deviation divided by square root of sample size = 15 / sqrt(11) = 4.522670169.<BR>\n" );
document.write( "at 95% two tailed confidence level, the critical t-score with 10 degrees of freedom is equal to plus or minus 2.228138842.<BR>\n" );
document.write( "use the t-score formula to find the equivalent raw score.<BR>\n" );
document.write( "on the high side, t = (x - m) / s becomes 2.228138842 = (x - 43) / 4.522670169.<BR>\n" );
document.write( "solve for x to get x = 2.228138842 * 4.522670169 + 43 = 53.07713707.<BR>\n" );
document.write( "on the low side, t = (x - m) / s becomes -2.228138842 = (x - 43) / 4.522670169.<BR>\n" );
document.write( "solve for x to get x = -2.228138842 * 4.522670169 + 43 = 32.92286293.<BR>\n" );
document.write( "your 95% confidence interval is from 32.92286293 to 53.07713707.<BR>\n" );
document.write( "in the t-score formula for this problem, .....<BR>\n" );
document.write( "t is the critical t-score<BR>\n" );
document.write( "x is the critical raw score<BR>\n" );
document.write( "m is the mean<BR>\n" );
document.write( "s is the standrd error. </SPAN>\n" );
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