document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1123349>Question 1123349</A>: <I><SPAN STYLE=\"word-break: break-all;\"> ``A simple sample of heights of 6400 Englishmen has a mean of 67.85 inches an a standard deviation of 2.56 inches, while a simple sample of heights of 1600 Australians has a mean of 68.55 inches and a standard deviation of 2.52 inches. Do the data indicate that Australians are on the average taller than Englishmen? Use 5% level of significance. Do it by z-test. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739646 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=739646\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> With large sample sizes, normality may be assumed if sample is random.<BR>\n" );
document.write( "Ho: Australians are same height or smaller<BR>\n" );
document.write( "Ha: Australians are taller.<BR>\n" );
document.write( "alpha=0.05 P{reject Ho|Ho true}<BR>\n" );
document.write( "1 way z-test<BR>\n" );
document.write( "critical value is z>1.645<BR>\n" );
document.write( "test (68.55-67.85)/sqrt (sd1^2/n1+sd2^2/n2); sqrt (0.004993)=0.0707<BR>\n" );
document.write( "z=(0.7)/0.0707=9.91<BR>\n" );
document.write( "reject Ho, highly significant<BR>\n" );
document.write( "Australians on average are taller than Englishmen. Note: with samples this large, the power to detect a difference is very large. Note: z-test is appropriate with samples this large.<BR>\n" );
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