document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206353>Question 1206353</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey, 13 people were asked how much they spent on their child's last birthday gift. The results were roughly bell-shaped with a mean of $35.6 and standard deviation of $3.3. Estimate how much a typical parent would spend on their child's birthday gift (use a 99% confidence level). Give your answers to 3 decimal places.\r<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 #843761 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=843761\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 13.<BR>\n" );
document.write( "sample mean is 35.6<BR>\n" );
document.write( "standard deviation is 3.3\r<BR>\n" );
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document.write( "tk-score formula is t = (x-m)/s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the critical sample mean<BR>\n" );
document.write( "m is the sample mean<BR>\n" );
document.write( "s is the standard error\r<BR>\n" );
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document.write( "at 99% two tail confidence interval with 12 degrees of freedom (sample size minus 1 = degrees of freedom in this problem), the critical t-score is equal to plus or minus t = 3.054540 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "s = standard error = standard deviation / sqrt(sample size) = 3.3 / sqrt(13) = .915255 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "t-score formula becomes plus or minus 3.054540 = (x - 35.6) / .915255.\r<BR>\n" );
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document.write( "on the high side of the confidence interval, solve for x to get x = 3.054540 * .915255 + 35.6 = 38.395683 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "on the low side of the confidence interval, solve for x to get x = -3.054540 * .915255 = 35.5 = 32.804317 rounded to 6 decimal places.\r<BR>\n" );
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document.write( "your solution is that the a typical parent would spend from 32.804 to 38.396 on their child's birthday, rounded to 3 decimal places, at 99% confidence interval.\r<BR>\n" );
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