document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1197083>Question 1197083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 2.	First-semester GPA’s for a random selection of freshmen at a large university are shown below. Estimate the true mean GPA of the frshman class with 99% confidence. Assume standard deviation = 0.62.<BR>\n" );
document.write( "1.9	3.2	2.0	2.9	2.7	3.3<BR>\n" );
document.write( "2.8	3.0	3.8	2.7	2.0	1.9<BR>\n" );
document.write( "2.5	2.7	2.8	3.2	3.0	3.8<BR>\n" );
document.write( "3.1	2.7	3.5	3.8	3.9	2.7<BR>\n" );
document.write( "2.0	2.8	1.9	4.0	2.2	2.8<BR>\n" );
document.write( "2.1	2.4	3.0	3.4	2.9	2.1<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 #830179 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3817)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=830179\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "Enter the given data into a spreadsheet.<BR>\n" );
document.write( "Let's say the upper left corner is in cell A1<BR>\n" );
document.write( "That places the bottom right corner in cell F6\r<BR>\n" );
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document.write( "In another blank cell off to the side somewhere, type in <font color=blue>=AVERAGE(A1:F6)</font> to find the arithmetic mean of this data set.<BR>\n" );
document.write( "Don't forget about the equal sign up front.<BR>\n" );
document.write( "The result should be roughly 2.819444<BR>\n" );
document.write( "This is the sample mean xbar.\r<BR>\n" );
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document.write( "If you wanted to find the value of xbar another way, then add up all the values and divide by 36 since there are 6*6 = 36 items in this list.<BR>\n" );
document.write( "The values add up to 101.5 which leads to xbar = 101.5/36 = 2.819444<BR>\n" );
document.write( "The command <font color=blue>=SUM(A1:F6)</font> will add up the values in cells A1 to F6.\r<BR>\n" );
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document.write( "At 99% confidence, the z critical value is roughly z = 2.576<BR>\n" );
document.write( "Use a table like this<BR>\n" );
document.write( "<a  rel=nofollow HREF= \"https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf\">https://www.sjsu.edu/faculty/gerstman/StatPrimer/t-table.pdf</a><BR>\n" );
document.write( "to get that value. Look at the bottom row labeled \"Z\" and above the 99% confidence level.\r<BR>\n" );
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document.write( "An alternative way to calculate this critical value is to type <font color=blue>=NORMINV((1-0.99)/2, 0, 1)</font> into the spreadsheet.<BR>\n" );
document.write( "The portion (1-0.99)/2 represents the area in each tail at 99% confidence.<BR>\n" );
document.write( "The spreadsheet should display -2.5758293035489, but we'll go with the positive version of that number.\r<BR>\n" );
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document.write( "We have this information<BR>\n" );
document.write( "z = 2.576 = critical value<BR>\n" );
document.write( "xbar = 2.819444 = approximate sample mean<BR>\n" );
document.write( "sigma = 0.62 = given population standard deviation<BR>\n" );
document.write( "n = 36 = sample size\r<BR>\n" );
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document.write( "Let's compute the margin of error<BR>\n" );
document.write( "E = z*sigma/sqrt(n)<BR>\n" );
document.write( "E = 2.576*0.62/sqrt(36)<BR>\n" );
document.write( "E = 0.266187\r<BR>\n" );
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document.write( "So,<BR>\n" );
document.write( "L = lower boundary<BR>\n" );
document.write( "L = xbar - E<BR>\n" );
document.write( "L = 2.819444 - 0.266187<BR>\n" );
document.write( "L = 2.553257<BR>\n" );
document.write( "L = 2.55<BR>\n" );
document.write( "and<BR>\n" );
document.write( "U = upper boundary<BR>\n" );
document.write( "U = xbar + E<BR>\n" );
document.write( "U = 2.819444 + 0.266187<BR>\n" );
document.write( "U = 3.085631<BR>\n" );
document.write( "U = 3.09\r<BR>\n" );
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document.write( "The 99% confidence interval for the population mean mu is roughly (2.55, 3.09)<BR>\n" );
document.write( "This is in the format (L, U)\r<BR>\n" );
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document.write( "This can be expressed as 2.55 < mu < 3.09 which is in the format L < mu < U\r<BR>\n" );
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document.write( "A third alternative is to say <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2.819444+%2B-++0.266187 ALIGN=MIDDLE  ALT=\"2.819444+%2B-++0.266187\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is in the format <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=xbar+%2B-+E ALIGN=MIDDLE  ALT=\"xbar+%2B-+E\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Round each value according to the instructions your teacher provides.<BR>\n" );
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