document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1200408>Question 1200408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Many people believe that the average number of Facebook friends is 338. The population standard deviation is 43.2. A random sample of 50 high school students in a particular district revealed that the average number of Facebook friends was 350. At alpha=0.05, is there sufficient evidence to conclude that the mean number of friends is greater than 338? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #834829 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><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=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=834829\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> population average is assumed to be 338.<BR>\n" );
document.write( "population standard deviation is 43.2<BR>\n" );
document.write( "sample of 50 students reveals that the average number of facebook friends is 350.<BR>\n" );
document.write( "test is to see if the average is greater than 338.<BR>\n" );
document.write( "one tailed alpha is indicated on the high end because the text is for greater than.<BR>\n" );
document.write( "at .05 alpha, on the high end, the critical z-score will be 1.644853626.<BR>\n" );
document.write( "z-score formula is z = (x-m)/s<BR>\n" );
document.write( "z is the z-score<BR>\n" );
document.write( "x is the sample mean<BR>\n" );
document.write( "m is the assumed population mean<BR>\n" );
document.write( "s is the standard error.<BR>\n" );
document.write( "standard error = standard deviation divided by square root of sample size = 43.2 / sqrt(50) = 6.209402589.<BR>\n" );
document.write( "test z-score = (350 - 338) / 6.209402589 = 1.964185503.<BR>\n" );
document.write( "since this is greater than the critical z-score, the test results are significant and the conclusion is that the verage is most probably greater than 338.<BR>\n" );
document.write( "you could also test with alpha.<BR>\n" );
document.write( "the results will be consistent with the critical z-score test.<BR>\n" );
document.write( "the critical alpha is .05 on the high end.<BR>\n" );
document.write( "the area to the right of the test z-score is .0247542216.<BR>\n" );
document.write( "since this is less than the critical alpha, the results are, once again, considered significant, leading to the same conclusion.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
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