document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1077656>Question 1077656</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The data in the table represent the ages of the winners of an award for the past five years. Use the data to answer questions&#8203; (a) through&#8203; (e).<BR>\n" );
document.write( "Data table: 61          36<BR>\n" );
document.write( "            31          31<BR>\n" );
document.write( "            50\r<BR>\n" );
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document.write( "a) compute the population mean\r<BR>\n" );
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document.write( "b)compute the mean for all 5C2=10 samples with a sample size of 2\r<BR>\n" );
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document.write( "c)Construct a sampling distribution for the mean by listing the sample mean and their corresponding probabilities. \r<BR>\n" );
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document.write( "d) compute the mean of the sampling distribution \r<BR>\n" );
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document.write( "Is anyone able to help and answer any of this? I'm so stuck on this problem, thank you! </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #692119 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=692119\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The mean of the population is 209/5=41.8<BR>\n" );
document.write( "The mean of all samples of n=2 will be:<BR>\n" );
document.write( "48.5<BR>\n" );
document.write( "46<BR>\n" );
document.write( "55.5<BR>\n" );
document.write( "46<BR>\n" );
document.write( "33.5<BR>\n" );
document.write( "31<BR>\n" );
document.write( "40.5<BR>\n" );
document.write( "43<BR>\n" );
document.write( "40.5<BR>\n" );
document.write( "33.5<BR>\n" );
document.write( "sum is 418, and mean is 41.8, same as the population mean.<BR>\n" );
document.write( "Each one of the 10 samples will be a point estimate of the sample mean.<BR>\n" );
document.write( "31 (0.1 probability)-3.1<BR>\n" );
document.write( "33.5 (0.2)----------6.7<BR>\n" );
document.write( "40.5 (0.2)----------8.1<BR>\n" );
document.write( "43 (0.1)------------4.3<BR>\n" );
document.write( "46 (0.2)------------9.2<BR>\n" );
document.write( "48.5 (0.1)----------4.85<BR>\n" );
document.write( "55.5 (0.1)----------5.55<BR>\n" );
document.write( "That sum is 41.8<BR>\n" );
document.write( "Not required but the standard deviation of the original population is 11.855<BR>\n" );
document.write( "The sd of the 10 samples is 7.26.  This turns out to be 11.855/sqrt(2), and this is a basic property of the sampling distribution from a population. It will have the same mean as the population, and its sd is sd of pop, or <BR>\n" );
document.write( "sigma/sqrt(n), the sample size.  This is one of the most important concepts in statistics. </SPAN>\n" );
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