document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=974224>Question 974224</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The recommended number of hours of sleep per night is 8 hours, but everybody \"knows\" that the average college student sleeps less than 7 hours. The number of hours slept last night by 10 randomly selected college students is listed below. Complete the following hypothesis test: Ho: &#956; = 7, Ha: &#956; < 7, &#945; = 0.05.\r<BR>\n" );
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document.write( "8	6.9	6.1	6.6	7.5	8	7.6	7.3	7.8	5.7\r<BR>\n" );
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document.write( "(a) Find t. (Give your answer correct to two decimal places.)<BR>\n" );
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document.write( "(ii) Find the p-value. (Give your answer correct to four decimal places.)<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 #596189 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=596189\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: mu >=7<BR>\n" );
document.write( "Ha: mu<7  The hypotheses must encompass the whole density function<BR>\n" );
document.write( "a=0.05  1 tail test<BR>\n" );
document.write( "Test statistic, t df=9<BR>\n" );
document.write( "Critical value t (df=9) < -1.833   ;; (xbar-mu)/s/sqrt(9);; 3 (xbar-mu)/s<BR>\n" );
document.write( "t=+0.5916  The mean is >7 (7.15), so the null hypothesis cannot be rejected a priori, since the data themselves show a mean greater than that which was postulated to be the maximum value.<BR>\n" );
document.write( "p=0.7157, but this is a calculated value, and again the fact that the mean is not in the range of Ha makes rejecting Ho impossible with this sample.\r<BR>\n" );
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document.write( "Note: if it were two-tailed, it still wouldn't be rejected.<BR>\n" );
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