document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=760434>Question 760434</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Given a sample of n1 = 40 from a population with known standard deviation &#963;1 =20, and an independent sample of n2 = 50 from another population with known standard deviation &#963;2 = 10, what is the value of the Z-test statistic for testing H0:  &#956;1 = &#956;2  (&#956;1 – &#956;2 = 0) if x-bar1 = 72 and x-bar2 = 66. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #462701 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=462701\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> the following definitions apply to this problem:\r<BR>\n" );
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document.write( "m1 = mean of sample 1<BR>\n" );
document.write( "s1 = standard deviation of population 1<BR>\n" );
document.write( "n1 = sample size of sample 1\r<BR>\n" );
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document.write( "m2 = mean of sample 2<BR>\n" );
document.write( "s2 = standard deviation of population 2<BR>\n" );
document.write( "n2 = sample size of sample 2\r<BR>\n" );
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document.write( "z = z-score of the difference between the mean of sample 1 and sample 2.\r<BR>\n" );
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document.write( "the standard error for this two sample z-test would be calculated as shown below as far as i know based on references from the web.\r<BR>\n" );
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document.write( "one such reference can be found  at <a  rel=nofollow HREF= \"http://www.stat.ucla.edu/~cochran/stat10/winter/lectures/lect21.html\" target = \"_blank\">http://www.stat.ucla.edu/~cochran/stat10/winter/lectures/lect21.html</a>\r<BR>\n" );
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document.write( "se = sqrt(s1^2/n1 + s2^2/n2)\r<BR>\n" );
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document.write( "you find s1^2/n1 and you find s2^2/n2 and you add them together and you then take the square root and you have the standard error for the test.\r<BR>\n" );
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document.write( "your numbers are:\r<BR>\n" );
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document.write( "m1 = 72, n1 = 40 s1 = 20<BR>\n" );
document.write( "m2 = 66, n2 = 50, s2 = 10\r<BR>\n" );
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document.write( "from this information, you calculate se as follows:\r<BR>\n" );
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document.write( "se = sqrt(20^2/40 + 10^2/50) = 3.4641\r<BR>\n" );
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document.write( "to find the z-score, you calculate m1 - m2 and then divide it by 3.4641 and you get:\r<BR>\n" );
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document.write( "z = (m1-m2) / se = (72-66) / 3.4641 = 6 / 3.4641 = 1.7321\r<BR>\n" );
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document.write( "note:\r<BR>\n" );
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document.write( "s1^2 means the variable with the name of s1 squared.<BR>\n" );
document.write( "likewise with s2<BR>\n" );
document.write( "m1-m2 means the variable with the name of m2 subtracted from the variable with the name of m1.\r<BR>\n" );
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document.write( " </SPAN>\n" );
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