document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1115160>Question 1115160</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A government-sponsored telephone counseling service for adolescents tested<BR>\n" );
document.write( "whether the length of calls would be affected by a special telephone system that<BR>\n" );
document.write( "had a better sound quality. Over the past several years, the lengths of telephone<BR>\n" );
document.write( "calls (in minutes) were normally distributed with  = 18 and  = 8. They<BR>\n" );
document.write( "arranged to have the special phone system loaned to them for one day. On that<BR>\n" );
document.write( "day, the mean length of the 46 calls they received was 21 minutes. Test whether<BR>\n" );
document.write( "the length of calls has changed using the 5% significance level. (a) Carry<BR>\n" );
document.write( "out a Z test using the five steps of hypothesis testing. (b) Make a drawing of<BR>\n" );
document.write( "the distributions involved. (c) Explain your answer to someone who knows<BR>\n" );
document.write( "about hypothesis testing with a sample of a single individual but who knows<BR>\n" );
document.write( "nothing about hypothesis testing with samples of more than one individual.<BR>\n" );
document.write( "(d) ADVANCED TOPIC: Figure the 95% confidence interval. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #730053 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=730053\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A government-sponsored telephone counseling service for adolescents tested<BR>\n" );
document.write( "whether the length of calls would be affected by a special telephone system that<BR>\n" );
document.write( "had a better sound quality. Over the past several years, the lengths of telephone<BR>\n" );
document.write( "calls (in minutes) were normally distributed with mu = 18 and sigma = 8. They<BR>\n" );
document.write( "arranged to have the special phone system loaned to them for one day. <BR>\n" );
document.write( "-----------------------<BR>\n" );
document.write( "On that day, the mean length of the 46 calls they received was 21 minutes. Test whether the length of calls has changed using the 5% significance level. <BR>\n" );
document.write( "(a) Carry out a Z test using the five steps of hypothesis testing.<BR>\n" );
document.write( "Ho: u1-u2 = 0<BR>\n" );
document.write( "Ha: u1-u2 # 0<BR>\n" );
document.write( "----<BR>\n" );
document.write( "sample difference:: 18-21 = -3<BR>\n" );
document.write( "reject intervals:: z< -1.96 and z > 1.96<BR>\n" );
document.write( "test statistic:: z(-3) = (-3)/sqrt[(8^2/n1^2)+(s2^2/n2)]<BR>\n" );
document.write( "Note:: n1, n2, and s2 are missing from your post.<BR>\n" );
document.write( "-------------------------- <BR>\n" );
document.write( "(b) Make a drawing of<BR>\n" );
document.write( "the distributions involved. (c) Explain your answer to someone who knows<BR>\n" );
document.write( "about hypothesis testing with a sample of a single individual but who knows<BR>\n" );
document.write( "nothing about hypothesis testing with samples of more than one individual.<BR>\n" );
document.write( "(d) ADVANCED TOPIC: Figure the 95% confidence interval.  </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );