document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199107>Question 1199107</A>: <I><SPAN STYLE=\"word-break: break-all;\"> We sampled 40 NY teachers for their annual income. In our sample,<BR>\n" );
document.write( "the average annual income is $60,000 and the standard deviation of annual<BR>\n" );
document.write( "incomes is $7,500. Based on that sample, we want to predict the mean annual<BR>\n" );
document.write( "income μ of all the NY teachers with the confidence level of 0.99 (99 percent).<BR>\n" );
document.write( "Part a) What is the error bound/margin E in our prediction about μ? <BR>\n" );
document.write( "Part b) What prediction do we make about μ? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #832809 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=832809\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the sample size is 40<BR>\n" );
document.write( "the sample mean is 60000.<BR>\n" );
document.write( "the sample standard deviation is 7500.\r<BR>\n" );
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document.write( "you would use the t-score to help solve this.<BR>\n" );
document.write( "the formula is t = (x-m)/s<BR>\n" );
document.write( "t is the t-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the population mean<BR>\n" );
document.write( "s is the standard error.\r<BR>\n" );
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document.write( "the standard error is equal to the standard deviation / square root of sample size = 7500 / sqrt(40) = 1185.854123.\r<BR>\n" );
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document.write( "at 99% confidence interval, you would calculate the two-tailed critical t-score with 39 degrees of freedom (sample size minus 1) to be plus or minus 2.707913179.\r<BR>\n" );
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document.write( "on the high side of the confidence interval, your t-score formula becomes:<BR>\n" );
document.write( "2.707913179 = (60000 - m) / 1185.854123.<BR>\n" );
document.write( "your margin of error on the high side is equal to (60000 - m) which is equal to 2.707913179 * 1185.854123 = 3211.190008.<BR>\n" );
document.write( "this indicates that your mean is 60000 - 3211.190008 = 56788.80999.\r<BR>\n" );
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document.write( "your solution should be:\r<BR>\n" );
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document.write( "Part a) What is the error bound/margin E in our prediction about μ?<BR>\n" );
document.write( "margin of error = 3211.19 rounded to 2 decimal places.\r<BR>\n" );
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document.write( "Part b) What prediction do we make about μ?<BR>\n" );
document.write( "population mean is assumed to be 56788.81 rounded to 2 decimal places.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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