document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=982171>Question 982171</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The dean of a university estimates that the mean number of classroom hours per week for&#8203; full-time faculty is 10.0. As a member of the student&#8203; council, you want to test this claim. A random sample of the number of classroom hours for 8 full-time faculty for one week is shown in the table below. At &#945;=0.10 can you reject the&#8203; dean's claim? Complete parts&#8203; (a) through&#8203; (c) below. <BR>\n" );
document.write( "Assume the population is normally distributed. <BR>\n" );
document.write( "10.3,8.2,11.3,6.5,4.9,9.6,14.1,8.8 \r<BR>\n" );
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document.write( "A. write the claim mathematically <BR>\n" );
document.write( "B. What is the P value? <BR>\n" );
document.write( "C. Decide whether to reject or fail to reject the null hypothesis. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #603028 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=603028\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A) The claim is mu = 10.0\r<BR>\n" );
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document.write( "The claim is the null hypothesis. The alternate hypothesis is mu =/= 10.0, so we have a two tailed test.\r<BR>\n" );
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document.write( "B)\r<BR>\n" );
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document.write( "Use a calculator to find that<BR>\n" );
document.write( "xbar = 9.2125<BR>\n" );
document.write( "s = 2.84677\r<BR>\n" );
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document.write( "Now compute the test statistic:\r<BR>\n" );
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document.write( "t = (xbar - mu)/(s/sqrt(n))<BR>\n" );
document.write( "t = (9.2125- 10)/(2.84677/sqrt(8))<BR>\n" );
document.write( "t = -0.78\r<BR>\n" );
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document.write( "Use either a table or a calculator to find that P(T < -0.78) = 0.23047 (the degrees of freedom equals n-1 = 8-1 = 7)\r<BR>\n" );
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document.write( "The p-value is therefore 2*0.23047 = 0.46094\r<BR>\n" );
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document.write( "C)\r<BR>\n" );
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document.write( "The p-value 0.46094 is larger than alpha = 0.10. So we fail to reject the null. We \"accept\" the claim that the mean mu is 10.0. We don't have enough evidence to overturn it. </SPAN>\n" );
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