document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=869677>Question 869677</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On the basis of her experience with clients, a clinical psychologist thinks that\r<BR>\n" );
document.write( "\n" );
document.write( "depression may interfere with sleep. She decided to test this idea. The sleep of nine \r<BR>\n" );
document.write( "\n" );
document.write( "depressed patients and eight normal controls is monitored for three successive nights. \r<BR>\n" );
document.write( "\n" );
document.write( "The average number of hours slept by each subject during the last two nights is shown \r<BR>\n" );
document.write( "\n" );
document.write( "Hours of sleep \r<BR>\n" );
document.write( "\n" );
document.write( "Depressed 9.2 7.5 3.9 7.1 6.1 6.6 7.4 7.4 5.9 \r<BR>\n" );
document.write( "\n" );
document.write( "Control 6.7 6.9 9.5 6.8 7.4 8.2 9.2 6.6 \r<BR>\n" );
document.write( "\n" );
document.write( "Is the clinician correct? Use &#945; = 0.05 in making your decision. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #524366 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=524366\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On the basis of her experience with clients, a clinical psychologist thinks that depression may interfere with sleep. <BR>\n" );
document.write( "She decided to test this idea. <BR>\n" );
document.write( "The sleep of nine depressed patients and eight normal controls is monitored for three successive nights. <BR>\n" );
document.write( "The average number of hours slept by each subject during the last two nights is shown. <BR>\n" );
document.write( "Hours of sleep <BR>\n" );
document.write( "Depressed 9.2 7.5 3.9 7.1 6.1 6.6 7.4 7.4 5.9 ::: mean = 6.82 with s = 1.47 <BR>\n" );
document.write( "Control 6.7 6.9 9.5 6.8 7.4 8.2 9.2 6.6:: mean = 7.66 with s = 1.16<BR>\n" );
document.write( "------------------------------------------  <BR>\n" );
document.write( "Is the clinician correct? Use &#945; = 0.05 in making your decision.<BR>\n" );
document.write( "Ho:: ud-uc >= 0<BR>\n" );
document.write( "Ha: ud - uc < 0<BR>\n" );
document.write( "====================<BR>\n" );
document.write( "sample stat:: ud - uc = 6.82-7.66 = -0.84<BR>\n" );
document.write( "----<BR>\n" );
document.write( "test stat:: t(-0.84) = (-0.84-0)/sqrt[(1.47^2/9)+(1.16^2/8)] = -1.3146<BR>\n" );
document.write( "=================<BR>\n" );
document.write( "p-value = P(t < -1.3146 when df = 9+8-2 = 15) = tcdf(-100,-1.3146,15) = 0.1042<BR>\n" );
document.write( "=====================<BR>\n" );
document.write( "Since the p-value is > 5%, fail to reject Ho.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Conclusion:: Depression makes no difference in amt. of sleep.<BR>\n" );
document.write( "==============<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
document.write( "\n" );
document.write( " <BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );