document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=335722>Question 335722</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The pre-med adviser of a liberal arts college is trying to determine the proportion of students entering the pre-med program who gain admission to medical school within 6 years of entering the program.<BR>\n" );
document.write( "a. If she does no preliminary study, how many former students from the pre-med program must she contact to be 90% sure that the point estimate is within 0.1 unit of p?<BR>\n" );
document.write( "b. A random sample of 36 former students from the pre-med program showed that 24 entered medical school within 6 years from the time they entered the program. How many more must she contact to be 90% sure that the point estimate is within 0.1 unit of p? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #240755 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=240755\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> a. If she does no preliminary study, how many former students from the pre-med program must she contact to be 90% sure that the point estimate is within 0.1 unit of p?<BR>\n" );
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document.write( "This implies you have no prior knowledge of the \"ball park\" level of the proportion of students gaining admission. In such cases, you use the conservative value of p=0.5 (because being Binomial in nature, its variance is highest at p=0.5)<BR>\n" );
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document.write( "formula for required sample size is derived from the Margin of Error for a Normal approximation:  <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=ME=+Z%2ASqrt%28p%2A%281-p%29%2Fn%29 ALIGN=MIDDLE  ALT=\"ME=+Z%2ASqrt%28p%2A%281-p%29%2Fn%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > and solving for n<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=Z%5E2%2Ap%2A%281-p%29%2F%28ME%29%5E2 ALIGN=MIDDLE  ALT=\"n=Z%5E2%2Ap%2A%281-p%29%2F%28ME%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Given 90% confidence and assuming Normal approximation, Z=-\+1.645<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=n=1.645%5E2%2A%280.5%2A%281-0.5%29%29%2F0.1%5E2=67.65 ALIGN=MIDDLE  ALT=\"n=1.645%5E2%2A%280.5%2A%281-0.5%29%29%2F0.1%5E2=67.65\"   DISABLED_style= \"max-width:90%; height:auto;\" > since we need whole numbers round up to 68<BR>\n" );
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document.write( "b. A random sample of 36 former students from the pre-med program showed that 24 entered medical school within 6 years from the time they entered the program. How many more must she contact to be 90% sure that the point estimate is within 0.1 unit of p?<BR>\n" );
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document.write( "Having done a preliminary study, you have prior \"ball park\" knowledge of p.<BR>\n" );
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document.write( "Same as part a) but substitute p=24/36=0.67 instead of p=0.5 </SPAN>\n" );
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