document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1085299>Question 1085299</A>: <I><SPAN STYLE=\"word-break: break-all;\"> SUPPOSE THAT A POPULATION PROPORTION IS .      40 AND THAT 80% OF THE TIME YOU DRAW A RANDOM SAMPLE FROM THIS POPULATION , YOU GET A SAMPLE PROPORTION OF 0.35 OR MORE. HOW LARGE A SAMPLE WERE YOU TAKING? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #699401 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=699401\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> what i get is this.\r<BR>\n" );
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document.write( "p = .4<BR>\n" );
document.write( "q = 1 - p = .6<BR>\n" );
document.write( "s = sqrt(p*q/n) = sqrt(.24/n)\r<BR>\n" );
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document.write( "p is the mean proportion which is also called m in the z-score formula<BR>\n" );
document.write( "q is 1 minus the mean proportion<BR>\n" );
document.write( "s is the standard deviation of the distribution of sample mean proportions\r<BR>\n" );
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document.write( "z = (x-m)/s = (.35-.4)/s = -.05/s\r<BR>\n" );
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document.write( "z is the z-score<BR>\n" );
document.write( "x is the proportion you are testing against the mean proportion.<BR>\n" );
document.write( "m is the mean proportion.<BR>\n" );
document.write( "s is the standard deviation of the distribution of sample mean proportions.\r<BR>\n" );
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document.write( "from z = -.05/s, solve for s to get s = -.05/z\r<BR>\n" );
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document.write( "if you get a score of .35 or more 80% of the time, then your alpha has to be .8\r<BR>\n" );
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document.write( "that would be 80% of the area under the normal distribution curve is to the right of that score.\r<BR>\n" );
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document.write( "this means 20% is to the left of that score.\r<BR>\n" );
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document.write( "solve for a z-score that has 20% of the area under the normal distribution curve to the left of that z-score and you get a z-score of -.8416212335\r<BR>\n" );
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document.write( "with a z-score of -.8416212335, the formula for s becomes:\r<BR>\n" );
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document.write( "s = -.05 / -.8416212335\r<BR>\n" );
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document.write( "we know that s is equal to sqrt(.24/n), so we get:\r<BR>\n" );
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document.write( "sqrt(.24/n) = (-.05 / -.8416212335)\r<BR>\n" );
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document.write( "square both sides of this equation to get:\r<BR>\n" );
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document.write( ".24/n = (-.05 / -.8416212335)^2\r<BR>\n" );
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document.write( "solve for n to get:\r<BR>\n" );
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document.write( "n = .24 / (-.05 / -.8416212335)^2\r<BR>\n" );
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document.write( "this results in n = 67.99932487\r<BR>\n" );
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document.write( "round this to 68.\r<BR>\n" );
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document.write( "your numbers become:\r<BR>\n" );
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document.write( "p = .4<BR>\n" );
document.write( "q = .6<BR>\n" );
document.write( "n = 68<BR>\n" );
document.write( "s = sqrt(.24/68) = .0594088526\r<BR>\n" );
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document.write( "z-score formula is z = (x-m)/s\r<BR>\n" );
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document.write( "this becomes z = (.35 - .4) / .0594088526 which results in:\r<BR>\n" );
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document.write( "z = -.8416254112\r<BR>\n" );
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document.write( "find the area of the normal distribution curve to the right of this z-score and you get:\r<BR>\n" );
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document.write( "alpha = .8000012235 which is slightly above 80%.\r<BR>\n" );
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document.write( "visually, it would look like this:\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2017/061905.jpg\" alt=\"$$$\" </> </SPAN>\n" );
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