document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1048478>Question 1048478</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Chi-square test of independence<BR>\n" );
document.write( "       Diploma--     No Diploma--   Total <BR>\n" );
document.write( "Male:          56--           32--             88<BR>\n" );
document.write( "Female:   62--          41--            103<BR>\n" );
document.write( "Total:      118--          73--             191<BR>\n" );
document.write( "a.Have the assumptions for this test been met? Why or why not?<BR>\n" );
document.write( "b.State the null and alternative hypotheses for this test.<BR>\n" );
document.write( "c. Calculate the test statistic for this test. Explain what this test statistic represents.<BR>\n" );
document.write( "d. What is the p-value? Explain what this p-value represents<BR>\n" );
document.write( "e. What is the conclusion for this test at the 0.05 level of significance. Are these variables dependent/associated? Why or why not? </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #664108 by </B><A HREF=/tutors/aboutme.mpl?userid=ewatrrr><B>ewatrrr(24785)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ewatrrr><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=ewatrrr><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=664108\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Diploma-- No Diploma-- Total <BR>\n" );
document.write( "Male: 56-- 32-- 88<BR>\n" );
document.write( "Female: 62-- 41-- 103<BR>\n" );
document.write( "Total: 118-- 73-- 191 <BR>\n" );
document.write( "a. Yes, random sampling, categorical variables and expected frequency counts > 5 <BR>\n" );
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document.write( "b.<BR>\n" );
document.write( "Ho : There is not a relationship between gender and whether or not someone is a college graduate (they are independent).<BR>\n" );
document.write( "Ha: There is a relationship between gender and whether or not someone is a college graduate (they are dependent). <BR>\n" );
document.write( "c.Apply Chi-square test for Independence<BR>\n" );
document.write( "(using the chi-square test for independence to determine whether gender is related to getting a diploma)<BR>\n" );
document.write( "E1,1 = (88 * 118) / 191 = 54.4, E1,2 = (88 * 73) / 191 = 33.6<BR>\n" );
document.write( "E2,1 = (103 * 118) / 191 = 63.6, E2,2 = (103 * 73) / 191 = 39.4<BR>\n" );
document.write( "X^2 = (56- 54.4)^2/54.4 + (32- 33.6)^2/33.6 + + (62 -63.6)^2/63.6 + (41 - 39.4)^2/39.4<BR>\n" );
document.write( "x^2 = .2282 = .23<BR>\n" );
document.write( "d. p-value is used to access the probability of X^2 having 1 degree of freedom is more extreme than .23<BR>\n" );
document.write( "DF is (r - 1) * (c - 1) = (2 - 1) * (2 - 1) = 1 (two rows, 2 columns) <BR>\n" );
document.write( "P(X^2 > .23) = 1 - .37 = .63<BR>\n" );
document.write( "e. 0.05 level of significance<BR>\n" );
document.write( ".63 > .05, accept Ho<BR>\n" );
document.write( " gender is NOT related to whether or not someone is a college graduate(they are independent).\r<BR>\n" );
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document.write( " </SPAN>\n" );
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