document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1183968>Question 1183968</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A random sample of 732 judges found that 405 were introverts. Construct a 95% confidence interval for the proportion. Interpret the meaning of the confidence interval. Justify your use of a confidence interval based on a normal distribution for data regarding proportions that are normally following a binomial distribution. (10 points) </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #814496 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=814496\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p hat, point estimate, is 405/732=0.5533<BR>\n" );
document.write( "half-interval for 95% Is z(0.975)*sqrt(0.5533*0.4467/732)<BR>\n" );
document.write( "=1.96*0.0184<BR>\n" );
document.write( "=0.0360<BR>\n" );
document.write( "the interval is  (0.5173, 0.5893)<BR>\n" );
document.write( "We are highly confident that the true value the proportion of judges who are introverts lies within this interval. </SPAN>\n" );
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