document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202937>Question 1202937</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A psychologist is interested in constructing a 99% confidence interval for the proportion of people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain. 54 of the 795 randomly selected people who were surveyed agreed with this theory. Round answers to 4 decimal places where possible.\r<BR>\n" );
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document.write( "With 99% confidence the proportion of all people who accept the theory that a person's spirit is no more than the complicated network of neurons in the brain is between </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838146 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=838146\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> p = 54/795 = .0679<BR>\n" );
document.write( "q = 1-p = 1-.0679 = .9321<BR>\n" );
document.write( "n = 795<BR>\n" );
document.write( "s = sqrt(p * q / n) = sqrt(.0679 * .9321 / 795) = .0089<BR>\n" );
document.write( "at 99% two tailed confidence interval, the critical z-score will be z = plus or minus 2.5758.<BR>\n" );
document.write( "when z = -2.5758, z = (x - .0679) / .0089.<BR>\n" );
document.write( "solve for x to get x = .0450.<BR>\n" );
document.write( "when z = 2.5758, z = (x - .0679) / .0089.<BR>\n" );
document.write( "solve for x to get x = .0908.<BR>\n" );
document.write( "your 99% confidence interval gets you a proportion from x = .0450 to x = .0908.<BR>\n" );
document.write( "that's the 99% confidence interval of the proportion of all people who accept the theory that a person's spirit is no more than the complicted network of neurons in the brain.\r<BR>\n" );
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document.write( "since the standard error was taken from the sample p rather than from the population p, it is possible that the use of the t-score was indicated rather than the use of the z-score.<BR>\n" );
document.write( "in that case, the critical t-score with 794 degrees of freedom would have been t = plus or minus 2.5820 and you would have gotten 99% confidence interval from x = .0449 to x = .0909.<BR>\n" );
document.write( "the difference would be very small because the sample size was quite large.\r<BR>\n" );
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document.write( "in most cases of this type, i've seen z being used, so a good bet would be to assume z is used whether or not the standrd error is taken from the assumed population p or from the sample p.\r<BR>\n" );
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document.write( "p is the proportion of all people who accept the theory that a person's spirit is no more than the complicted network of neurons in the brain.<BR>\n" );
document.write( "q is the roportion of all people who don't belie that.<BR>\n" );
document.write( "n is the sample size<BR>\n" );
document.write( "dof = degrees of freedom for use in t-score analysis = n - 1.<BR>\n" );
document.write( "s = standard error = sqrt(p * q / n)\r<BR>\n" );
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