document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1061776>Question 1061776</A>: <I><SPAN STYLE=\"word-break: break-all;\"> According to a 2010 Business Week article, the average 401(k) account balance for individuals nearing 										<BR>\n" );
document.write( "retirement was $60,000.  To test if this average has recently changed, suppose a sample of 30 people										<BR>\n" );
document.write( "starting retirement was selected and it found that the average 401(k) balance was $67,000.  Assume the										<BR>\n" );
document.write( "population standard deviation was $21,000.  Using an &#945; = .05, answer the following:										<BR>\n" );
document.write( "										<BR>\n" );
document.write( "a.     State the null and alternative hypotheses.										<BR>\n" );
document.write( "b.     What conclusions can be made about the current average balance of 401(k) accounts for 										<BR>\n" );
document.write( "        people nearing retirement?										<BR>\n" );
document.write( "c.     Determine the p-value for this test and interpret its meaning.										<BR>\n" );
document.write( "d.     Repeat the preceding hypothesis test using the critical value approach.										<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #677212 by </B><A HREF=/tutors/aboutme.mpl?userid=Boreal><B>Boreal(15235)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Boreal><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/cgi-bin/show-face.mpl?user=Boreal><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=677212\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Ho: There has been no change mu o=mu<BR>\n" );
document.write( "Ha: There has bee a change mu o ne mu<BR>\n" );
document.write( "alpha=0.05 prob reject Ho|Ho is true<BR>\n" );
document.write( "test statistic is z.<BR>\n" );
document.write( "critical value is |z|>1.96<BR>\n" );
document.write( "calculation z=(x bar-mean)/sigma/sqrt(30)<BR>\n" );
document.write( "t=7000*sqrt(30)/21000=(1/3)*sqrt(30)=1.83<BR>\n" );
document.write( "This is not greater than 1.96<BR>\n" );
document.write( "Fail to reject Ho: insufficient evidence to say that there was a change.<BR>\n" );
document.write( "p-value=0.068. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );