document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1175516>Question 1175516</A>: <I><SPAN STYLE=\"word-break: break-all;\"> (Give your answers correct to TWO (2) decimal places)\r<BR>\n" );
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document.write( "In a time and motion study, the amount of time required to paint a 10-foot by 10-foot room is measured for 25 painters. The sample mean is calculated and  found to be 72 minutes. If we assume that the population standard deviation is 5 minutes,\r<BR>\n" );
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document.write( "(a)  find the 95% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room.\r<BR>\n" );
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document.write( "Answer:the 95% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room is from ____ minutes to ____minutes.\r<BR>\n" );
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document.write( "(b)  find  the 97% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room.\r<BR>\n" );
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document.write( "Answer:  the 97% confidence interval estimate of the mean time for all painters to paint a 10-foot by 10-foot room is from____ minutes to____minutes. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #803603 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=803603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> sample size is 25<BR>\n" );
document.write( "sample mean is 72 minutes<BR>\n" );
document.write( "population standard deviation is 5 minutes.\r<BR>\n" );
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document.write( "standard error = standard deviation / square root of sample size = 5 / sqrt(25) = 5/5 = 1.\r<BR>\n" );
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document.write( "z-score = (x - m) / s\r<BR>\n" );
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document.write( "x is the raw score<BR>\n" );
document.write( "m is the raw mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "at two tailed confidence level, the tails on each end of the confidence interval are 2.5%.\r<BR>\n" );
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document.write( "the critical z-score is therefore equal to plus or minus 1.96.\r<BR>\n" );
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document.write( "solve for the high raw score as follows:\r<BR>\n" );
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document.write( "start with 1.96 = (x - 72) / 1\r<BR>\n" );
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document.write( "solve for x to get x = 1.96 * 1 + 72 = 73.96.\r<BR>\n" );
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document.write( "solve for the low raw score as follows:\r<BR>\n" );
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document.write( "start with -1.96 = (x - 72) / 1\r<BR>\n" );
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document.write( "solve for x to get x = -1.96 * 1 + 72 = 70.04\r<BR>\n" );
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document.write( "your answer for question (a) is 70.04 to 73.96 minutes.\r<BR>\n" );
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document.write( "with a two tailed 97% confidence level, the tails on each end of the confidence interval are 1.5%.\r<BR>\n" );
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document.write( "the critical z-score becomes plus or minus 2.17.\r<BR>\n" );
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document.write( "solve for the low and high raw score in the same manner as you did the the 95% confidence interval.\r<BR>\n" );
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document.write( "you will get the low score equal to 69.83 and the high score equal to 74.17.\r<BR>\n" );
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document.write( "visually, this looks like this.\r<BR>\n" );
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document.write( "first 95% confidence interval, then 97% confidence interval.\r<BR>\n" );
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document.write( "when dealing with the mean of a sample, you do not use the standard deviation.\r<BR>\n" );
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document.write( "you use the standard error.\r<BR>\n" );
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document.write( "the standard error is defined as the standard deviation of the distribution of sample means.\r<BR>\n" );
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document.write( "here's a reference.\r<BR>\n" );
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document.write( "<a  rel=nofollow HREF= \"https://www.investopedia.com/terms/s/standard-error.asp\" target = \"_blank\">https://www.investopedia.com/terms/s/standard-error.asp</a>\r<BR>\n" );
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document.write( " </SPAN>\n" );
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