document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=981083>Question 981083</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Population 1 had a standard deviation of 8 and population 2 had a standard deviation of 10. In a random sample of 30 units from Population 1, the mean was 50. In a random sample of 40 units from Population 2, the mean was 48. Perform a test of hypothesis to investigate whether Population 1 has a greater mean compared to Population 2. Use a significance level of 0.05. Use z as test statistic.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #602113 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=602113\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Given:<BR>\n" );
document.write( "n1 = 30<BR>\n" );
document.write( "xbar1 = 50<BR>\n" );
document.write( "sigma1 = 8\r<BR>\n" );
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document.write( "n2 = 40<BR>\n" );
document.write( "xbar2 = 48<BR>\n" );
document.write( "sigma2 = 10\r<BR>\n" );
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document.write( "Hypothesis:<BR>\n" );
document.write( "H0: mu1 <= mu2<BR>\n" );
document.write( "H1: mu1 > mu2\r<BR>\n" );
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document.write( "Right tailed test. Reject H0 if the test statistic z is larger than critical value\r<BR>\n" );
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document.write( "Standard Error:<BR>\n" );
document.write( "SE = sqrt(((sigma1)^2)/(n1)+((sigma2)^2)/(n2))<BR>\n" );
document.write( "SE = sqrt((8^2)/(30)+(10^2)/(40))<BR>\n" );
document.write( "SE = 2.1525179\r<BR>\n" );
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document.write( "Test Statistic:<BR>\n" );
document.write( "z=((xbar1-xbar2)-(mu1-mu2))/(SE)<BR>\n" );
document.write( "z=((50-48)-0)/(2.1525179)<BR>\n" );
document.write( "z=0.9291444<BR>\n" );
document.write( "z=0.93\r<BR>\n" );
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document.write( "When alpha = 0.05, the critical value is 1.645 for a right tailed test.\r<BR>\n" );
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document.write( "The test statistic is NOT larger than the critical value. So we fail to reject the null hypothesis. The p-value (0.1764) is larger than alpha. This also tells us to fail to reject the null.\r<BR>\n" );
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document.write( "Decision: Fail to reject H0. Effectively the null hypothesis is \"accepted\"\r<BR>\n" );
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document.write( "Interpretation: Population 1 does not have a greater mean than population 2. </SPAN>\n" );
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