document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=392762>Question 392762</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 percentage signal change of 58. From many previous<BR>\n" );
document.write( "studies with this same math problems procedure (but not listening to music), it is<BR>\n" );
document.write( "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. (a) Using the .01 level, what should<BR>\n" );
document.write( "the researcher conclude? Solve this problem explicitly using all five steps of hypothesis<BR>\n" );
document.write( "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 distribution.<BR>\n" );
document.write( "(b) Then explain your answer to someone who has never had a course in statistics<BR>\n" );
document.write( "(but who is familiar with mean, standard deviation, and Z scores). </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #278823 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=278823\">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<BR>\n" );
document.write( "make a particular brain area more active. (that is the claim)<BR>\n" );
document.write( "------------------------- <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 percentage signal change of 58. (that is the sample mean)<BR>\n" );
document.write( "------------------------- <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( "(that is the population data)<BR>\n" );
document.write( "---------------------------\r<BR>\n" );
document.write( "\n" );
document.write( "(a) Using the .01 level, what should the researcher conclude? <BR>\n" );
document.write( "Solve this problem explicitly using all five steps of hypothesis<BR>\n" );
document.write( "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 distribution.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Ho: u = 35<BR>\n" );
document.write( "Ha: u > 35 (claim)<BR>\n" );
document.write( "---<BR>\n" );
document.write( "z(58) = (58-35)/10 = 23/10 = 2.3<BR>\n" );
document.write( "---<BR>\n" );
document.write( "The critical region for a right tail test with alpha = 1% is z>2.3263<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Conclusion: Since the test statistic is less than z = 2.3263, reject Ho.<BR>\n" );
document.write( "The test results support the claim.<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Cautionary Note.  Since the test statistic is barely in the reject interval<BR>\n" );
document.write( "more testing is required.<BR>\n" );
document.write( "================================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( "(b) Then explain your answer to someone who has never had a course in statistics<BR>\n" );
document.write( "(but who is familiar with mean, standard deviation, and Z scores).<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );