document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1072430>Question 1072430</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A small town has 2500 families. the average number of children per family is 3.2, with a standard deviation of 0.5; the distribution is skewed. A researcher wants to draw a random sample of 100 families from the small town and record the number of children in each family. Her statistical inference would be based on a sampling distribution pf all possible samples of size 100. <BR>\n" );
document.write( "(a) What is the mean of the sampling data?<BR>\n" );
document.write( "(b) What is the standard deviation of the sampling distribution of all possible sample means?<BR>\n" );
document.write( "(c) What is the shape of the sampling distribution of all possible sample means? Explain why </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #687345 by </B><A HREF=/tutors/aboutme.mpl?userid=rothauserc><B>rothauserc(4718)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=rothauserc><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=rothauserc><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=687345\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The sample size is 100 / 2500 = 1/25 of the population which is a significant proportion of the population.<BR>\n" );
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document.write( "a) the mean of the sample  is the same as the population mean which is 3.2<BR>\n" );
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document.write( "b) the standard deviation of the sampling distribution(SE) is calculated with the following formula<BR>\n" );
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document.write( "standard error(SE) = (0.5 / square root(100)) * square root( (2500 - 100) / (2500 - 1))<BR>\n" );
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document.write( "SE = 0.0495<BR>\n" );
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document.write( "c) since the population distribution is skewed, we need sample size > 40 to ensure that the sample distribution approximates a normal distribution<BR>\n" );
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