document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199178>Question 1199178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a survey of 225 randomly selected gun owners, it was found that 69 of them said they owned a gun primarily for protection.\r<BR>\n" );
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document.write( "Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Report answers to at least 2 decimal places. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833061 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=833061\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size = 225<BR>\n" );
document.write( "p = 69/225 <BR>\n" );
document.write( "q = (1 - 69) / 225 = 225/225 - 69/225 = (225 - 69) / 225 = 156/225<BR>\n" );
document.write( "mean = 69/225<BR>\n" );
document.write( "standard error = sqrt(p*q/n) = sqrt((69/225*156/225)/225) = .0307406515.<BR>\n" );
document.write( "z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "(x-m) is the margin of error.<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "your confidence interval is 95%.<BR>\n" );
document.write( "at 95% confidence interval, the critical z-score is plus or minus 1.96\r<BR>\n" );
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document.write( "to find the margin of error, you only need to use the hi side z-score because the confidence interval is symmetric about the mean and the margin of error above the mean is the same as the margin of error below the mean.\r<BR>\n" );
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document.write( "formula becomes 1.96 = (x-m) / standard error which becomes 1.96 = (x-m) / .0307406515.\r<BR>\n" );
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document.write( "solve for (x-m) to get (x-m) = 1.96 * .0307406515 = .0602516769.\r<BR>\n" );
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document.write( "that should be the margin of error on either side of the mean at 95% confidence interval.\r<BR>\n" );
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document.write( "the mean is equal to 69/225<BR>\n" );
document.write( "that minus the margin of error yields a low side value of .2464149897.<BR>\n" );
document.write( "that plus the margin of error yields a high side value of .3669183436.\r<BR>\n" );
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document.write( "this is tested using the calculator at <a  rel=nofollow HREF= \"https://davidmlane.com/hyperstat/z_table.html\" target = \"_blank\">https://davidmlane.com/hyperstat/z_table.html</a>\r<BR>\n" );
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document.write( "below are the results.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121608.jpg\">\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" src = \"http://theo.x10hosting.com/2022/121609.jpg\">\r<BR>\n" );
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document.write( "your solution is shown below:\r<BR>\n" );
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document.write( "the margin of error is .0602516769 at 95% confidence interval.\r<BR>\n" );
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document.write( "the 95% confidence interval is from .2464149897 to .3669183436.\r<BR>\n" );
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document.write( "let me know if you have any questions.<BR>\n" );
document.write( "theo\r<BR>\n" );
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document.write( " </SPAN>\n" );
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