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 #843762 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=843762\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Answer: <font color=red>(32.804, 38.396)</font><BR>\n" );
document.write( "It is equivalent to writing 32.804 < mu < 38.396\r<BR>\n" );
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document.write( "Explanation\r<BR>\n" );
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document.write( "n = 13 = sample size<BR>\n" );
document.write( "xbar = 35.6 = sample mean<BR>\n" );
document.write( "s = 3.3 = sample standard deviation<BR>\n" );
document.write( "sigma = population standard deviation = unknown\r<BR>\n" );
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document.write( "Because we don't know the value of sigma, and because n > 30 is not the case, we must use the T distribution.\r<BR>\n" );
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document.write( "df = degrees of freedom<BR>\n" );
document.write( "df = n-1<BR>\n" );
document.write( "df = 13-1<BR>\n" );
document.write( "df = 12\r<BR>\n" );
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document.write( "Use a T table such as this one<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "or one found on any other websites, or one found in the back of your stats textbook.<BR>\n" );
document.write( "For exam purposes, your teacher is likely to hand out such a table if s/he expected you to use it.\r<BR>\n" );
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document.write( "Locate the row that starts with df = 12.<BR>\n" );
document.write( "The column we want will have \"confidence level = 99%\" labeled at the bottom. <BR>\n" );
document.write( "The intersection of this row and column leads to 3.055 which is the approximate t critical value.<BR>\n" );
document.write( "It means that P(-3.055 < T < 3.055) = 0.99 approximately when df = 12.\r<BR>\n" );
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document.write( "Many online stats calculators can be used as an alternative to determine the t critical value.<BR>\n" );
document.write( "Or you could use a TI84 or similar<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.statology.org/how-to-find-the-t-critical-value-on-a-ti-84-calculator/\">https://www.statology.org/how-to-find-the-t-critical-value-on-a-ti-84-calculator/</a>\r<BR>\n" );
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document.write( "Here are the key values we need<BR>\n" );
document.write( "xbar = 35.6<BR>\n" );
document.write( "s = 3.3 <BR>\n" );
document.write( "n = 13<BR>\n" );
document.write( "t = 3.055 (approximate)\r<BR>\n" );
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document.write( "Then,<BR>\n" );
document.write( "E = margin of error<BR>\n" );
document.write( "E = t*s/sqrt(n)<BR>\n" );
document.write( "E = 3.055*3.3/sqrt(13)<BR>\n" );
document.write( "E = 2.796105<BR>\n" );
document.write( "which is approximate\r<BR>\n" );
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document.write( "Now we can compute the lower bound and upper bound.<BR>\n" );
document.write( "L = lower bound<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 35.6 - 2.796105<BR>\n" );
document.write( "L = 32.803895<BR>\n" );
document.write( "L = 32.804\r<BR>\n" );
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document.write( "U = upper bound<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 35.6 + 2.796105<BR>\n" );
document.write( "U = 38.396105<BR>\n" );
document.write( "U = 38.396\r<BR>\n" );
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document.write( "The 99% confidence interval of the form L < mu < U would be roughly 32.804 < mu < 38.396<BR>\n" );
document.write( "That condenses to the notation (32.804, 38.396)\r<BR>\n" );
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document.write( "Some textbooks will use the notation [32.804, 38.396] which represents the same thing more or less.<BR>\n" );
document.write( "The fact we include endpoints or not isn't really important to the confidence interval overall.\r<BR>\n" );
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document.write( "Here is a calculator you can use to check your work<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.socscistatistics.com/confidenceinterval/default2.aspx\">https://www.socscistatistics.com/confidenceinterval/default2.aspx</a><BR>\n" );
document.write( "and here's another similar resource<BR>\n" );
document.write( "<a  rel=nofollow HREF=\"https://www.statology.org/confidence-intervals-ti-84-calculator/\">https://www.statology.org/confidence-intervals-ti-84-calculator/</a><BR>\n" );
document.write( "The function you want is called <font color=red>TInterval</font><BR>\n" );
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