document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1207888>Question 1207888</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1. To estimate with 95% confidence the average number of kilometres that students living off-campus commute to classes every day, a random sample of 20 students was taken and produced a mean equal to 5.2 km and a standard deviation of 3.05 km. Under these circumstances, what is the appropriate critical value?<BR>\n" );
document.write( "a. 2.093<BR>\n" );
document.write( "b. 1.960    <BR>\n" );
document.write( "c. 2.086<BR>\n" );
document.write( "d. 1.729 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #846017 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=846017\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "n = 20 = sample size<BR>\n" );
document.write( "xbar = 5.2 = sample mean<BR>\n" );
document.write( "s = 3.05 = sample standard deviation<BR>\n" );
document.write( "sigma = population standard deviation = unknown\r<BR>\n" );
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document.write( "We don't know the value of sigma and n > 30 is not the case, so we must use the T distribution.<BR>\n" );
document.write( "df = degrees of freedom<BR>\n" );
document.write( "df = n-1<BR>\n" );
document.write( "df = 20-1<BR>\n" );
document.write( "df = 19\r<BR>\n" );
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document.write( "You could use a stats calculator like a TI83 to find the T critical value.<BR>\n" );
document.write( "However, I'll use a T table such as 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( "Such a table can be found at the back of your stats textbook.<BR>\n" );
document.write( "Highlight the df = 19 row and the column that mentions \"confidence level = 95%\" (mentioned at the bottom of the table)<BR>\n" );
document.write( "The intersection of this row and column yields the approximate t critical value t = <font color=red>2.093</font>\r<BR>\n" );
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document.write( "What does this tell us?<BR>\n" );
document.write( "It tells us that P(-2.093 < t < 2.093) = 0.95 approximately when df = 19.<BR>\n" );
document.write( "The 0.95 is the area of the main body while 1-0.95 = 0.05 is the combined area of the two tails.<BR>\n" );
document.write( "The 0.95 refers to the confidence level 95%.\r<BR>\n" );
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document.write( "The final answer is <font color=red>option A</font><BR>\n" );
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