document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170272>Question 1170272</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In a study of brain waves during sleep, a sample of 29 college students were randomly<BR>\n" );
document.write( "separated into two groups. The first group had 15 people and each was given ½ liter of<BR>\n" );
document.write( "red wine before sleeping. The second group had 14 people and were given no alcohol<BR>\n" );
document.write( "before sleeping. All participants when to sleep at 11 PM and their brainwave activity was<BR>\n" );
document.write( "measured from 4-6 AM. The group drinking alcohol had a mean brainwave activity of<BR>\n" );
document.write( "19.65 hertz and a standard deviation of 1.86 hertz. The group not drinking alcohol had a<BR>\n" );
document.write( "mean of 6.59 hertz and standard deviation of 1.91 hertz. Compute a 90% confidence<BR>\n" );
document.write( "interval for the difference in population means of groups drinking alcohol before<BR>\n" );
document.write( "sleeping and those not drinking alcohol before sleeping. Explain the meaning of the<BR>\n" );
document.write( "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 #795169 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=795169\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the half-interval is t (0.95, df=27)* sqrt((s1^2/n1+(s2^2/n2))<BR>\n" );
document.write( "=1.703*sqrt(0.4912)<BR>\n" );
document.write( "=1.19<BR>\n" );
document.write( "the difference between the two means is (19.65-6.59)=13.06<BR>\n" );
document.write( "so the 90%CI is (11.87, 14.25) hertz<BR>\n" );
document.write( "This means that we are highly confident that the difference between the mean EEG frequency with and without alcohol is not 0 but rather positive.  Were the differences not significant, 0 would have been contained in the confidence interval. The true difference is not known, but we are highly confident it lies in this interval (90% confident).  It is not a probability, since the parameter exists, if unknown and not knowable, and therefore either lies in the interval or doesn't.\r<BR>\n" );
document.write( "\n" );
document.write( "{alcohol and other sedative drugs produce alpha rhythm, which is a fast rhythm, whereas normal sleep produces low frequency delta waves.) </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );