document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=141841>Question 141841</A>: <I><SPAN STYLE=\"word-break: break-all;\"> On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof.<BR>\n" );
document.write( "Hardtack that he is really a 90+ performer but this sample just happened to fall below his true<BR>\n" );
document.write( "performance level. (a) State an appropriate pair of hypotheses. (b) State the formula for the test<BR>\n" );
document.write( "statistic and show your decision rule using the 1 percent level of significance. (c) Carry out the<BR>\n" );
document.write( "test. Show your work. (d) What assumptions are required? (e) Use Excel to find the p-value and<BR>\n" );
document.write( "interpret it.<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 #103390 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=103390\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> On eight Friday quizzes, Bob received scores of 80, 85, 95, 92, 89, 84, 90, 92. He tells Prof. Hardtack that he is really a 90+ performer but this sample just happened to fall below his true performance level. <BR>\n" );
document.write( "(a) State an appropriate pair of hypotheses.<BR>\n" );
document.write( "Ho: u>= 90<BR>\n" );
document.write( "H1: u < 90<BR>\n" );
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document.write( "(b) State the formula for the test statistic and show your decision rule using<BR>\n" );
document.write( "the 1 percent level of significance.<BR>\n" );
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document.write( "Critical value for df= 7 and alpha=1% : t=-2.998<BR>\n" );
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document.write( "Find the sample mean: 88.375<BR>\n" );
document.write( "and standard deviation: 4.9839<BR>\n" );
document.write( "(c) Carry out the test. Show your work. <BR>\n" );
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document.write( "t(88.375) = (88.375-90)/[4.9839/sqrt(8)] = -0.9222...<BR>\n" );
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document.write( "(d) What assumptions are required? <BR>\n" );
document.write( "Check in your textbook<BR>\n" );
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document.write( "(e) Use Excel to find the p-value and interpret it.<BR>\n" );
document.write( "p-value = P(-10 < t < -0.9222) = 0.1935..<BR>\n" );
document.write( "The probability the test results could have given stronger evidence<BR>\n" );
document.write( "for rejecting Ho is 19.35%; therefore fail to reject Ho.<BR>\n" );
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document.write( "cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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