document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1206894>Question 1206894</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Assume that a sample is used to estimate a population proportion p. Find the 90% confidence interval for a sample of size 341 with 74% successes. Enter your answer as an open-interval (i.e., parentheses) using decimals (not percents) accurate to three decimal places.\r<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 #844597 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=844597\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 341. .023<BR>\n" );
document.write( "p = .74<BR>\n" );
document.write( "q = 1 - .74 = .26\r<BR>\n" );
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document.write( "sample proportion mean is .74<BR>\n" );
document.write( "sample standard error = sqrt(p * q / n) = sqrt(.74*.26/341) = .02375 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "critical z-score at 90% two tail confidence interval is equal to plus or minus 1.64485 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "z-score formula of z = (x-m)/s is used.<BR>\n" );
document.write( "in this problem:<BR>\n" );
document.write( "z = z-score z-score<BR>\n" );
document.write( "x = critical raw score<BR>\n" );
document.write( "m = mean proportion<BR>\n" );
document.write( "s = standard error\r<BR>\n" );
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document.write( "on the high side, z-score formula becomes 1.64485 = (x - .74) / .02375.<BR>\n" );
document.write( "solve for x to get x = 1.64485 * .02375 + .74 = .779 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "on the low side, z-score formula becomes -1.64485 = (x - .74) / .02375.<BR>\n" );
document.write( "solve for x to get x = -1.64485 * .02375 + .75 = .701 rounded to 3 decimal places.\r<BR>\n" );
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document.write( "your 90% interval is from .701 to .779.<BR>\n" );
document.write( "that's your solution.<BR>\n" );
document.write( "i believe that's going to be (.701,.779) in interval form.\r<BR>\n" );
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