document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200393>Question 1200393</A>: <I><SPAN STYLE=\"word-break: break-all;\"> If n=440 and X = 352, construct a 99% confidence interval.\r<BR>\n" );
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document.write( "Give your answers to three decimals\r<BR>\n" );
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document.write( " ______< p <_______ <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 #845046 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=845046\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "The other tutor has made a few mistakes. <ul><li>The value of phat is not 0.</li><li>We're calculating a confidence interval estimating the population proportion p, and not the population mean mu.</li><li>Because of the previous bullet point, we use the Z distribution instead of T distribution.</li></ul>Here is the proper way to solve this problem.<BR>\n" );
document.write( "phat = sample proportion<BR>\n" );
document.write( "phat = (number of successes)/(sample size)<BR>\n" );
document.write( "phat = x/n<BR>\n" );
document.write( "phat = 352/440<BR>\n" );
document.write( "phat = 0.8 exactly<BR>\n" );
document.write( "This is the center of the confidence interval.<BR>\n" );
document.write( "The job of phat is to estimate the population proportion p.\r<BR>\n" );
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document.write( "At 99% confidence, the z critical value is roughly z = 2.576<BR>\n" );
document.write( "This value is to either be memorized or looked up on a reference sheet.<BR>\n" );
document.write( "The back of your stats textbook will have the necessary table of values.<BR>\n" );
document.write( "Your stats professor may let you have a notecard for exams, or perhaps hand out reference sheets for exams.\r<BR>\n" );
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document.write( "E = margin of error for a proportion<BR>\n" );
document.write( "E = z*sqrt(phat*(1-phat)/n)<BR>\n" );
document.write( "E = 2.576*sqrt(0.8*(1-0.8)/440)<BR>\n" );
document.write( "E = 0.049122392598 approximately<BR>\n" );
document.write( "E = 0.049122\r<BR>\n" );
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document.write( "L = lower boundary of confidence interval<BR>\n" );
document.write( "L = phat - E<BR>\n" );
document.write( "L = 0.8 - 0.049122<BR>\n" );
document.write( "L = 0.750878<BR>\n" );
document.write( "L = 0.751\r<BR>\n" );
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document.write( "U = upper boundary of confidence interval<BR>\n" );
document.write( "U = phat + E<BR>\n" );
document.write( "U = 0.8 + 0.049122<BR>\n" );
document.write( "U = 0.849122<BR>\n" );
document.write( "U = 0.849\r<BR>\n" );
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document.write( "The values of L and U are approximate.\r<BR>\n" );
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document.write( "The 99% confidence interval of the format L < p < U is therefore approximately <font color=red>0.751 < p < 0.849</font> when rounding to 3 decimal places.<BR>\n" );
document.write( "Many stats calculators can be used to confirm this solution.<BR>\n" );
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