document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=333318>Question 333318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> After sampling from two binomial populations, we found the following:\r<BR>\n" );
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document.write( "p = 0.48 n1 = 100 p2 = 0.052 n2 =100\r<BR>\n" );
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document.write( "if we estimate with 90% confidence the difference in population proportions, what would be the outome?    <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 #238879 by </B><A HREF=/tutors/aboutme.mpl?userid=jrfrunner><B>jrfrunner(365)</B></A><img src=\"/images/stars/stars-10.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jrfrunner><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=jrfrunner><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=238879\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> you can apply the binomial method directly which can be tedious and difficult<BR>\n" );
document.write( "or \"if\" the assumptions are met, can apply a normal approximation to the binomial.<BR>\n" );
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document.write( "The enable the use of the normal approximation, the following need to be met<BR>\n" );
document.write( "1. <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D%2Ap%5B1%5D%3E5 ALIGN=MIDDLE  ALT=\"n%5B1%5D%2Ap%5B1%5D%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D%2Ap%5B2%5D%3E5 ALIGN=MIDDLE  ALT=\"n%5B2%5D%2Ap%5B2%5D%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B1%5D%2A%281-p%5B1%5D%29%3E5 ALIGN=MIDDLE  ALT=\"n%5B1%5D%2A%281-p%5B1%5D%29%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n%5B2%5D%2A%281-p%5B2%5D%29%3E5 ALIGN=MIDDLE  ALT=\"n%5B2%5D%2A%281-p%5B2%5D%29%3E5\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you provided p1 = 0.48 n1 = 100 p2 = 0.052 n2 =100 <BR>\n" );
document.write( "NOTE: not sure if your p2 is correct.  Nevertheless, it looks like the requirements above are met.<BR>\n" );
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document.write( "90% confidence interval for difference in the population proportions yields Z=1.645<BR>\n" );
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document.write( "Upper confidence interval value:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5B1%5D-p%5B2%5D%29+%2B+Z%2ASqrt%28p%5B1%5D%2A%281-p%5B1%5D%29%2Fn%5B1%5D+%2Bp%5B2%5D%2A%281-p%5B2%5D%29%2Fn%5B2%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Lower confidence interval value:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28p%5B1%5D-p%5B2%5D%29+-+Z%2ASqrt%28p%5B1%5D%2A%281-p%5B1%5D%29%2Fn%5B1%5D+%2Bp%5B2%5D%2A%281-p%5B2%5D%29%2Fn%5B2%5D%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "confidence interval = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.48-0.052%29-1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29 ALIGN=MIDDLE  ALT=\"%280.48-0.052%29-1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%280.48-0.052%29%2B1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29 ALIGN=MIDDLE  ALT=\"%280.48-0.052%29%2B1.645%2Asqrt%280.48%2A0.52%2F100%2B0.052%2A0.948%2F100%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you can do the math </SPAN>\n" );
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