document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=170658>Question 170658</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/9780072966930/algebrahomeworkh></A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Ages for the 2005 Boston Red Sox pitchers are shown below. (a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work. (b) If there is a difference, is it important? (c) Find the p-value and interpret it.\r<BR>\n" );
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document.write( "Ages of Boston Red Sox Pitchers, October 2005 \r<BR>\n" );
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document.write( "Arroyo 28    Foulke  33      Mantei 32<BR>\n" );
document.write( "Timlin 39    Clement 31      Gonzalez 30<BR>\n" );
document.write( "Miller 29    Wakefield 39    Embree   35<BR>\n" );
document.write( "Halama 33    Myers     36    Wells    42<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 #126177 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=126177\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ages for the 2005 Boston Red Sox pitchers are shown below. <BR>\n" );
document.write( "(a) Assuming this is a random sample of major league pitchers, at the 5 percent level of significance does this sample show that the true mean age of all American League pitchers is over 30 years? State your hypotheses and decision rule and show all work.<BR>\n" );
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document.write( "Ho: u <=30<BR>\n" );
document.write( "Ha: u > 30<BR>\n" );
document.write( "Using a one tail z test with alpha = 5%: z = -1.645<BR>\n" );
document.write( "The sample mean =  28.89<BR>\n" );
document.write( "z(28.89) = (28.89-30)/10.2646 = -0.1081<BR>\n" );
document.write( "This z-value is not in the rejection region so \"Fail to reject Ho\".<BR>\n" );
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document.write( "(b) If there is a difference, is it important?<BR>\n" );
document.write( "There is a slight difference but it is not important.<BR>\n" );
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document.write( "(c) Find the p-value and interpret it.<BR>\n" );
document.write( "p-value = 0.457<BR>\n" );
document.write( "There is a 45.7% probability that test results could result<BR>\n" );
document.write( "in stronger evidence to reject Ho.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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document.write( "Ages of Boston Red Sox Pitchers, October 2005 <BR>\n" );
document.write( "Arroyo 28 Foulke 33 Mantei 32<BR>\n" );
document.write( "Timlin 39 Clement 31 Gonzalez 30<BR>\n" );
document.write( "Miller 29 Wakefield 39 Embree 35<BR>\n" );
document.write( "Halama 33 Myers 36 Wells 42<BR>\n" );
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