document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=446385>Question 446385</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A researcher knows that the population mean among college students taking the Social Conformity Test is a \"neutral\" 100. (scores higher than 100 are assumed to represent more conformity than average, and those lower than 100 indicate less conformity). A random sample of 30 students was selected, and the following values were recorded:<BR>\n" );
document.write( "sample mean = 103<BR>\n" );
document.write( "sample standard deviation= 10.83<BR>\n" );
document.write( "Is this sample significantly different than the population?<BR>\n" );
document.write( "State the null and alternative hypotheses.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #307414 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=307414\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A researcher knows that the population mean among college students taking the Social Conformity Test is a \"neutral\" 100. (scores higher than 100 are assumed to represent more conformity than average, and those lower than 100 indicate less conformity).<BR>\n" );
document.write( " A random sample of 30 students was selected, and the following values were recorded:<BR>\n" );
document.write( "sample mean = 103<BR>\n" );
document.write( "sample standard deviation= 10.83<BR>\n" );
document.write( "Is this sample significantly different than the population?<BR>\n" );
document.write( "State the null and alternative hypotheses. <BR>\n" );
document.write( "----<BR>\n" );
document.write( "Ho: u = 100<BR>\n" );
document.write( "Ha: u is not equal to 100 (the sample is significantly different)<BR>\n" );
document.write( "---------<BR>\n" );
document.write( "t(103) = (103-100)/[10.83/sqrt(30)] = 1.5172..<BR>\n" );
document.write( "---<BR>\n" );
document.write( "p-value = 2P(t>1.5172 when df = 29) == 2*0.07 = 14%<BR>\n" );
document.write( "----<BR>\n" );
document.write( "Since the p-value is greater than 5%, fail to reject<BR>\n" );
document.write( "Ho at the 5% level of significance.<BR>\n" );
document.write( "The sample is not significantly different than the population.<BR>\n" );
document.write( "===========================<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );