document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=188882>Question 188882</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the Real Estate Board of Greater Vancouver conducts a study of the number of first-time applicants who are successful in passing the certification examination for real estate salespeople on their first attempt. Two samples were taken from the list of applicants: those who were already employed by a real estate agency and those who were recent university graduates who had not taken a full-time job. Results are shown in the table below:\r<BR>\n" );
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document.write( "	           Real Estate Employees	Unemployed Graduates<BR>\n" );
document.write( "Sample Size                 100                         200<BR>\n" );
document.write( "Number passing	             47                         102\r<BR>\n" );
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document.write( "a.What is the sample proportion of real estate employees who passed the exam on their first attempt?<BR>\n" );
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document.write( "b.What is the sample proportion of unemployed college graduates who passed the exam on their first attempt?<BR>\n" );
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document.write( "c.If the null hypothesis is H0: &#61552;R – &#61552;U = 0, what is the value of the test statistic? &#61552;R = proportion of real estate employees passing the exam on their first attempt, &#61552;U  = proportion of unemployed graduates passing the exam on their first attempt.<BR>\n" );
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document.write( "d. State your conclusion on the result of the test for H0: &#61552;R – &#61552;U = 0 if the alternate hypothesis is: H0: &#61552;R – &#61552;U < 0. Use &#61537; = 0.05.<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #141656 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=141656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> -----------------<BR>\n" );
document.write( "Suppose the Real Estate Board of Greater Vancouver conducts a study of the number of first-time applicants who are successful in passing the certification examination for real estate salespeople on their first attempt.<BR>\n" );
document.write( "Two samples were taken from the list of applicants: those who were already employed by a real estate agency and those who were recent university graduates who had not taken a full-time job. <BR>\n" );
document.write( "Results are shown in the table below: <BR>\n" );
document.write( "Real Estate Employees Unemployed Graduates<BR>\n" );
document.write( "Sample Size 100 200<BR>\n" );
document.write( "Number passing 47 102 \r<BR>\n" );
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document.write( "a.What is the sample proportion of real estate employees who passed the exam on their first attempt?<BR>\n" );
document.write( "47/100 = 0.47<BR>\n" );
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document.write( "b.What is the sample proportion of unemployed college graduates who passed the exam on their first attempt?<BR>\n" );
document.write( "102/200 = 0.51<BR>\n" );
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document.write( "c.If the null hypothesis is Ho: pR – pU = 0, what is the value of the test statistic? pR = proportion of real estate employees passing the exam on their first attempt, &#61552;U = proportion of unemployed graduates passing the exam on their first attempt.<BR>\n" );
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document.write( "z(0.47-0.51) = -0.04/sqrt[(.5*.5/100) + (.5*.5/200)] = -0.6532<BR>\n" );
document.write( "p-value = P(-100 < z < -0.6532) = 0.2568<BR>\n" );
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document.write( "d. State your conclusion on the result of the test for H0: &#61552;R – &#61552;U = 0 if the alternate hypothesis is: H0: &#61552;R – &#61552;U < 0. Use &#61537; = 0.05.<BR>\n" );
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document.write( "Since the p-value is greater than 5%, fail to reject Ho.<BR>\n" );
document.write( "The population proportions of the two groups are statistically the same.<BR>\n" );
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document.write( "If there are parts of this you do not understand you should ask<BR>\n" );
document.write( "for clarification.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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