document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1202823>Question 1202823</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ighTech Incorporated randomly tests its employees about company policies. Last year in the 510 random tests conducted, 16 employees failed the test.\r<BR>\n" );
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document.write( "a. What is the point estimate of the population proportion that failed the test? <BR>\n" );
document.write( "b. What is the margin of error for a 95% confidence interval estimate? <BR>\n" );
document.write( "c. Compute the 95% confidence interval for the population proportion. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838056 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=838056\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> best i can make out of this based on what's given is:\r<BR>\n" );
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document.write( "p = mean failure rate = 16 / 510 = .03137.<BR>\n" );
document.write( "q = (1 - p) - (1 - 16 / 510) = (1 - .03137) = .96863.\r<BR>\n" );
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document.write( "point estimate of the population proportion that failed the test is 16 / 510 = .03137 rounded to 5 decimal places.\r<BR>\n" );
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document.write( "standard error for a proportion is equal to sqrt (p * q / n) which is equal to sqrt(.03137 * .96863 / 510) = .00772.\r<BR>\n" );
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document.write( "margin of error for 95% confidence interval of the mean failure rate would be based on the critical z-score of plus or minus 1.96.\r<BR>\n" );
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document.write( "formula becomes 1.96 = (x - .03137) / .00772.<BR>\n" );
document.write( "solve for (x - .03137) to get:<BR>\n" );
document.write( "(x - .03137) = 1.96 * .00772 = .01513.<BR>\n" );
document.write( "that's your margin of error.\r<BR>\n" );
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document.write( "solve for x in that same formula to get:<BR>\n" );
document.write( "x = 1.96 * .00772 + .03157 = .0465012.<BR>\n" );
document.write( "that would be the high side of the interval.\r<BR>\n" );
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document.write( "the low side of the interval would be equal to -1.96 * .00772 + .031357 = .01623388.\r<BR>\n" );
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document.write( "answers to your questions would be, as far as i can tell.\r<BR>\n" );
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document.write( "a. What is the point estimate of the population proportion that failed the test?<BR>\n" );
document.write( ".03137\r<BR>\n" );
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document.write( "b. What is the margin of error for a 95% confidence interval estimate?<BR>\n" );
document.write( ".01513\r<BR>\n" );
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document.write( "c. Compute the 95% confidence interval for the population proportion.<BR>\n" );
document.write( ".0162388 to .0465012.\r<BR>\n" );
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document.write( "this is the best that i can do, based on what i know.<BR>\n" );
document.write( "the mean failure rate was 16/510.<BR>\n" );
document.write( "the 95% confidence interval was based on that as the mean.\r<BR>\n" );
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document.write( "let me know is you have any questions.<BR>\n" );
document.write( "theo<BR>\n" );
document.write( " </SPAN>\n" );
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