document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1190937>Question 1190937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> what is the mean and standard deviation of the sampling distribution of proportions respectively, given that n=100 and p= 0.5 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #822689 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</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=822689\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "p = 0.5 is the population proportion<BR>\n" );
document.write( "Each various sample proportion is denoted as <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \hat{p}\"><BR>\n" );
document.write( "The symbol <IMG STYLE=\"max-width:80%;\" SRC=\"/cgi-bin/rendertex.cgi?\large \hat{p}\"> can be written as \"p-hat\" or \"phat\" because the letter p has a hat on top.<BR>\n" );
document.write( "The \"ph\" isn't sounded out as an \"f\" sound. The \"p\" is separate from the \"hat\".\r<BR>\n" );
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document.write( "The sample distribution consists of random phat values based on repeated samplings of the population.<BR>\n" );
document.write( "In this case, we're sampling 100 individuals to compute the phat values.\r<BR>\n" );
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document.write( "The phat distribution will have a mean of p = 0.5 because the phat values will fall on either side of this center. The more data points, the better the picture will come into focus that the center is 0.5<BR>\n" );
document.write( "This is all due to the fact the sampling distribution is clustered around the population parameter.\r<BR>\n" );
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document.write( "The standard deviation for the phat values isn't as simple unfortunately.<BR>\n" );
document.write( "The good news is that the formula isn't too crazy.<BR>\n" );
document.write( "sigma = sqrt(p*(1-p)/n)<BR>\n" );
document.write( "sigma = sqrt(0.5*(1-0.5)/100)<BR>\n" );
document.write( "sigma = sqrt(0.5*0.5/100)<BR>\n" );
document.write( "sigma = sqrt(0.25/100)<BR>\n" );
document.write( "sigma = sqrt(0.0025)<BR>\n" );
document.write( "sigma = 0.05\r<BR>\n" );
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document.write( "Here's where you can find more info<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://online.stat.psu.edu/stat500/lesson/4/4.2/4.2.2\">https://online.stat.psu.edu/stat500/lesson/4/4.2/4.2.2</a><BR>\n" );
document.write( "and here's a page with a similar example problem to get more practice<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/sampling-distribution-proportion/e/sampling-distribution-sample-proportion-mean-standard-deviation\">https://www.khanacademy.org/math/ap-statistics/sampling-distribution-ap/sampling-distribution-proportion/e/sampling-distribution-sample-proportion-mean-standard-deviation</a>\r<BR>\n" );
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document.write( "Answers:<BR>\n" );
document.write( "mean = 0.5<BR>\n" );
document.write( "standard deviation = 0.05<BR>\n" );
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