document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1129450>Question 1129450</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a random sample of 24 &#8203;people, the mean commute time to work was 30.8 minutes and the standard deviation was 7.1 minutes. Assume the population is normally distributed and use a&#8203; t-distribution to construct a 95&#8203;% confidence interval for the population mean mu. What is the margin of error of mu&#8203;? Interpret the results.<BR>\n" );
document.write( "The confidence interval for the population mean mu is left parenthesis comma  right parenthesis .<BR>\n" );
document.write( "&#8203;(Round to one decimal place as&#8203; needed.)<BR>\n" );
document.write( "The margin of error of mean is:<BR>\n" );
document.write( "  <BR>\n" );
document.write( "&#8203;(Round to one decimal place as&#8203; needed.)<BR>\n" );
document.write( "Interpret the results.<BR>\n" );
document.write( "A.<BR>\n" );
document.write( "It can be said that 95&#8203;% of people have a commute time between the bounds of the confidence interval.<BR>\n" );
document.write( "B.<BR>\n" );
document.write( "With 95&#8203;% &#8203;confidence, it can be said that the commute time is between the bounds of the confidence interval.<BR>\n" );
document.write( "C.<BR>\n" );
document.write( "With 95&#8203;% &#8203;confidence, it can be said that the population mean commute time is between the bounds of the confidence interval.<BR>\n" );
document.write( "D.<BR>\n" );
document.write( "If a large sample of people are taken approximately 95&#8203;% of them will have commute times between the bounds of the confidence interval. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #746032 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=746032\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> t df=23,0.975=2.069<BR>\n" );
document.write( "s=7.1<BR>\n" );
document.write( "ts/sqrt(n) is half interval or 2.069*7.1/sqrt(24)=3.0 ANSWER<BR>\n" );
document.write( "(27.8, 33.8)units minutes\r<BR>\n" );
document.write( "\n" );
document.write( "C <BR>\n" );
document.write( "The purpose of a confidence interval is to define where the true mean lies, with a certain degree of confidence.  The true mean is usually unknown and unknowable and either lies in or out of the interval.  We don't know which, and it is a 100-0 type of issue, which is why we use confidence for where we think the true mean lies, not a probability. </SPAN>\n" );
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