document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=310137>Question 310137</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Evolutionary theories often emphasize that humans have adapted to their physical<BR>\n" );
document.write( "environment. One such theory hypothesizes that people should spontaneously<BR>\n" );
document.write( "follow a 24-hour cycle of sleeping and waking—even if they are not exposed to<BR>\n" );
document.write( "the usual pattern of sunlight. To test this notion, eight paid volunteers were<BR>\n" );
document.write( "placed (individually) in a room in which there was no light from the outside and<BR>\n" );
document.write( "no clocks or other indications of time. They could turn the lights on and off as<BR>\n" );
document.write( "they wished. After a month in the room, each individual tended to develop a<BR>\n" );
document.write( "steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.\r<BR>\n" );
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document.write( "Using the .05 level of significance, what should we conclude about the<BR>\n" );
document.write( "theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved. (c) Explain your answer to someone who has never taken a course in statistics.<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 #221839 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=221839\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25.<BR>\n" );
document.write( "x-bar = 25 ; s = 1.1952<BR>\n" );
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document.write( "Using the .05 level of significance, what should we conclude about the<BR>\n" );
document.write( "theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?) <BR>\n" );
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document.write( "(a) Use the steps of hypothesis testing.<BR>\n" );
document.write( "Ho: u = 24<BR>\n" );
document.write( "Ha: u is not equal to 24<BR>\n" );
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document.write( "t(25) = (25-24)/[1.1952/sqrt(8)] = 2.3665<BR>\n" );
document.write( "p-value = 2P(t> 2.3665 with df=7) = 2*0.0249 = 0.0499<BR>\n" );
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document.write( "Conclusion: At the 5% significance level, reject Ho<BR>\n" );
document.write( "because the p-value is less than 5%.<BR>\n" );
document.write( "Note: They don't get any closer than this.\r<BR>\n" );
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document.write( "(b) Sketch the distributions involved.<BR>\n" );
document.write( "Have to leave that to you.<BR>\n" );
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document.write( "(c) Explain your answer to someone who has never taken a course in statistics.<BR>\n" );
document.write( "Have to leave that to you.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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