document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=211120>Question 211120</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher predicts that listening to music while solving math problems will<BR>\n" );
document.write( "make a particular brain area more active. To test this, a research participant has<BR>\n" );
document.write( "her brain scanned while listening to music and solving math problems, and the<BR>\n" );
document.write( "brain area of interest has a percent signal change of 58. From many previous<BR>\n" );
document.write( "studies with this same math-problems procedure (but not listening to music), it<BR>\n" );
document.write( "is known that the signal change in this brain area is normally distributed with a<BR>\n" );
document.write( "mean of 35 and a standard deviation of 10. Using the .01 level, what should the<BR>\n" );
document.write( "researcher conclude? Solve this problem explicitly using all five steps of<BR>\n" );
document.write( "hypothesis testing, and illustrate your answer with a sketch showing the comparison<BR>\n" );
document.write( "distribution, the cutoff (or cutoffs), and the score of the sample on this<BR>\n" );
document.write( "distribution. Then explain your answer to someone who has never had a course<BR>\n" );
document.write( "in statistics (but who is familiar with mean, standard deviation, and Z score </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #159518 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=159518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> problems will make a particular brain area more active. <BR>\n" );
document.write( "To test this, a research participant has her brain scanned while listening to music and solving math problems, and the brain area of interest has a percent signal change of 58. <BR>\n" );
document.write( "From many previous studies with this same math-problems procedure (but not listening to music), it is known that the signal change in this brain area is normally distributed with a mean of 35 and a standard deviation of 10. <BR>\n" );
document.write( "Using the .01 level, what should the researcher conclude?<BR>\n" );
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document.write( "Ho: u = 35<BR>\n" );
document.write( "Ha: u > 35<BR>\n" );
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document.write( "Critical Value: z = 2.326<BR>\n" );
document.write( "Test statistic: z = (35-58)/10 = 2.3<BR>\n" );
document.write( "p-value = P(z>2.3) = 0.0107<BR>\n" );
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document.write( "Since the p-value is greater than 1%, do not reject Ho<BR>\n" );
document.write( "But the decision is very close. More testing should be done.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );