document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1187957>Question 1187957</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A monograph written in 1902 states that the mean height of adult American males is 67.0 inches with a standard deviation of 3.5 inches. Wishing to see if these values have changed over the twentieth century the geneticist measured a random sample of 28 adult American males and found that X = 69.4 inches and s = 4.0 inches. Are these values significantly different from the values published in 1902 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #819016 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=819016\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> this is a 1 sample t-test<BR>\n" );
document.write( "Can do this as a confidence interval assuming that the sd of the sample is an unbiased estimator of that of the population. The CI of a sample of 28 in this example would contain 3.5, that of the population, so a 1-sample t-test and t-interval could be done.<BR>\n" );
document.write( "t-test<BR>\n" );
document.write( "Ho; mean is 67.0<BR>\n" );
document.write( "Ha: mean is not 67.0<BR>\n" );
document.write( "alpha=0.05 p{reject Ho|Ho true}<BR>\n" );
document.write( "test is a t 0.975 df=27<BR>\n" );
document.write( "critical value is |t| > 2.052<BR>\n" );
document.write( "t=(69.4-67)/4/sqrt(28)<BR>\n" );
document.write( "=3.17<BR>\n" );
document.write( "reject Ho, the height is more<BR>\n" );
document.write( "p-value=0.0037<BR>\n" );
document.write( "-<BR>\n" );
document.write( "half-interval is mean +/- t(0.975, df=27)s/sqrt(n) for a 95% interval]<BR>\n" );
document.write( "=2.052*4.0/sqrt(28)<BR>\n" );
document.write( "=1.55<BR>\n" );
document.write( "the 95% t-interval is (67.85, 70.95)<BR>\n" );
document.write( "Since 67.0 is not in the interval, there values are significantly different.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );