document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188113>Question 188113</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher predicts that listening to music while solving math problems will make a particular brain area more active. 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. 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. Using the .01 level, what should the researcher conclude? Solve this problem explicitly using all five steps of hypothesis testing, and illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution. Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores).\r<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 #141171 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=141171\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A researcher predicts that listening to music while solving math problems will make a particular brain area more active. 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" );
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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" );
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document.write( "Using the .01 level, what should the researcher conclude?<BR>\n" );
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document.write( "Solve this problem explicitly using all five steps of hypothesis testing<BR>\n" );
document.write( "Ho: u = 0.35<BR>\n" );
document.write( "Ha: u is not equal to 0.0.35<BR>\n" );
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document.write( "z(0.58) = (0.58-0.35)/0.10 = 2.3<BR>\n" );
document.write( "p-value = 2P(z > 2.3) = 0.0214<BR>\n" );
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document.write( "Conclusion: since the p-value is greater than 1%, Fail to reject Ho.<BR>\n" );
document.write( "The result of this one test is not sufficient evidence to reject <BR>\n" );
document.write( "the belief that the mean percentage is 0.35.<BR>\n" );
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document.write( "Illustrate your answer with a sketch showing the comparison distribution, the cutoff (or cutoffs), and the score of the sample on this distribution.<BR>\n" );
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document.write( "This site does not support graphing normal distributions and marking those<BR>\n" );
document.write( "illustrations.<BR>\n" );
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document.write( " Then explain your answer to someone who has never had a course in statistics (but who is familiar with mean, standard deviation, and Z scores). <BR>\n" );
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document.write( "I hope ou can handle this last.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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