document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=977550>Question 977550</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following data show the number of hours studied for an exam, x, and the grade received on the exam, y (y is measured in 10's; that is, y = 8 means that the grade, rounded to the nearest 10 points, is 80).<BR>\n" );
document.write( "x	2	3	3	3	3	4	4	5	5	6	6	7	8	8	8\r<BR>\n" );
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document.write( "y	5	5	6	7	8	7	9	7	8	7	9	10	8	9	10<BR>\n" );
document.write( "Using the estimated standard error of regression, sb1 = 0.1435, for the number of hours studied–exam grade relationship, find the 95% confidence interval for the population slope &#946;1. The equation for the line of best fit was y = 4.83 + 0.57x. (Give your answers correct to three decimal places.)\r<BR>\n" );
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document.write( "lower limit:<BR>\n" );
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document.write( "upper limit:<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 #599198 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=599198\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> y = 4.83 + 0.57x has the slope 0.57. This is the estimate of the population slope &#946;1. Let's call m the estimate of the population slope.\r<BR>\n" );
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document.write( "n = 15<BR>\n" );
document.write( "df = n-1 = 14\r<BR>\n" );
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document.write( "Critical Value (95% confidence, df = 14). Use <a  rel=nofollow HREF=\"http://www.itl.nist.gov/div898/handbook/eda/section3/eda3672.htm\">this table</a><BR>\n" );
document.write( "t = 2.145\r<BR>\n" );
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document.write( "Margin of Error (ME)<BR>\n" );
document.write( "ME = t*Sb1 = 2.145*0.1435 = 0.3078075<BR>\n" );
document.write( "ME = 0.3078075\r<BR>\n" );
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document.write( "Lower Bound (L)<BR>\n" );
document.write( "L = m - ME<BR>\n" );
document.write( "L = 0.57 - 0.3078075<BR>\n" );
document.write( "L = 0.2621925<BR>\n" );
document.write( "L = 0.262\r<BR>\n" );
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document.write( "Upper Bound (U)<BR>\n" );
document.write( "U = m + ME<BR>\n" );
document.write( "U = 0.57 + 0.3078075<BR>\n" );
document.write( "U = 0.8778075<BR>\n" );
document.write( "U = 0.878\r<BR>\n" );
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document.write( "Summary:\r<BR>\n" );
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document.write( "lower limit: <font color=\"red\">0.262</font>\r<BR>\n" );
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document.write( "upper limit: <font color=\"red\">0.878</font>\r<BR>\n" );
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document.write( "The 95% confidence interval for the slope &#946;1 is <font color=\"red\">(0.262, 0.878)</font> </SPAN>\n" );
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