document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190595>Question 1190595</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SAMPLING DISTRIBUTION WITH AND WITHOUT REPLACEMENT\r<BR>\n" );
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document.write( "A population consists of (3,8,10,15). Consider all possible sample size 2 that can be drawn with replacement.\r<BR>\n" );
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document.write( "-what is the standard deviation of the sampling distribution of means? =\r<BR>\n" );
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document.write( "-what is the population mean? =\r<BR>\n" );
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document.write( "-what is the population standard deviation? =\r<BR>\n" );
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document.write( "-what is the population variance? =\r<BR>\n" );
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document.write( "-what is the variance of the sampling distribution of means? =\r<BR>\n" );
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document.write( "-what is the mean of the sampling distribution of means? =\r<BR>\n" );
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document.write( "A population consists of (3,8,10,15). Consider all possible sample size<BR>\n" );
document.write( " 2 that can be drawn without replacement.\r<BR>\n" );
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document.write( "-what is the variance of the sampling distribution of means? =\r<BR>\n" );
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document.write( "-what is the standard deviation of the sampling distribution of means? =\r<BR>\n" );
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document.write( "-what is the mean of the sampling distribution of means? =<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 #822320 by </B><A HREF=/tutors/aboutme.mpl?userid=MathLover1><B>MathLover1(20849)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=MathLover1><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=MathLover1><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=822320\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a.<BR>\n" );
document.write( "what is the population mean?\r<BR>\n" );
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document.write( " We have population values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >,  population size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=4+ ALIGN=MIDDLE  ALT=\"N=4+\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=mu=%283%2B8%2B10%2B15%29%2F4=9 ALIGN=MIDDLE  ALT=\"mu=%283%2B8%2B10%2B15%29%2F4=9\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "what is the population variance? \r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta%5E2=%281%2F4%29%28%283-9%29%5E2%2B%288-9%29%5E2%2B%2810-9%29%5E2+%2B%2815-9%29%5E2%29=18.5%2B%2815-9%29%5E2%29=18.5 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "c.<BR>\n" );
document.write( "what is the population standard deviation?\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=delta=+sqrt%28delta%5E2%29=sqrt%2818.5%29 ALIGN=MIDDLE  ALT=\"delta=+sqrt%28delta%5E2%29=sqrt%2818.5%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ≈<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.3012 ALIGN=MIDDLE  ALT=\"4.3012\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "d. We have population values <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=8 ALIGN=MIDDLE  ALT=\"8\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=10 ALIGN=MIDDLE  ALT=\"10\"   DISABLED_style= \"max-width:90%; height:auto;\" >,<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=15 ALIGN=MIDDLE  ALT=\"15\"   DISABLED_style= \"max-width:90%; height:auto;\" >, population size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=N=4 ALIGN=MIDDLE  ALT=\"N=4\"   DISABLED_style= \"max-width:90%; height:auto;\" > and sample size <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=2 ALIGN=MIDDLE  ALT=\"n=2\"   DISABLED_style= \"max-width:90%; height:auto;\" >. \r<BR>\n" );
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document.write( "Thus, the number of possible samples which can be drawn without replacement is\r<BR>\n" );
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document.write( "​<BR>\n" );
document.write( "  what is the mean of the sampling distribution of means? \r<BR>\n" );
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document.write( "​The mean of the sampling distribution of the sample means is equal to the the mean of the population.<BR>\n" );
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