document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=139460>Question 139460</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Stan, please explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence.  Please provide an example of using one of these hypothesis test.  Please be specifc providing the steps to the hypothesis test in your exmaple.<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 #101679 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=101679\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> explain the characteristics of a Chi-Square Goodness of Fit hypothesis test as well as the Chi-Square test for independence.  Please provide an example of using one of these hypothesis test.  Please be specifc providing the steps to the hypothesis test in your exmaple.<BR>\n" );
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document.write( "These are large topics. You would have to see a text on statistics or use<BR>\n" );
document.write( "Google to get all of what you are looking for.  But here is a little of it.<BR>\n" );
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document.write( "Goodness of Fit with a simplified example:<BR>\n" );
document.write( "30 horse races are run with horses in 3 lanes.<BR>\n" );
document.write( "# of wins from lane  DISABLED_event_one=  8<BR>\n" );
document.write( "# of wins from lane two = 12<BR>\n" );
document.write( "# of wins from lane three = 10<BR>\n" );
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document.write( "Ho: It makes no difference which lane the horse starts in.<BR>\n" );
document.write( "Ha: It makes a difference.<BR>\n" );
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document.write( "Comment: If it makes no difference there should be 10 wins from each position.<BR>\n" );
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document.write( "Run a Chi-Sq on a 2 x 3 Matrix:<BR>\n" );
document.write( "row 1: 8....12....10<BR>\n" );
document.write( "row 2: 10...10....10<BR>\n" );
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document.write( "Chi-Sq results:<BR>\n" );
document.write( "Test statistic: Chi-Sq = 0.404040404...<BR>\n" );
document.write( "p-value: 0.81707<BR>\n" );
document.write( "df=2<BR>\n" );
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document.write( "Conclusion: Since p-value is greater than 5%, Fail to reject Ho.<BR>\n" );
document.write( "It makes no difference which lane the horse starts in.<BR>\n" );
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document.write( "Ch-Sq Test for Independence<BR>\n" );
document.write( "You have three horses, A, B, C and you have three lanes on the track 1,2.3.<BR>\n" );
document.write( "You keep track of how many wins each horse has on each track.<BR>\n" );
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document.write( "------------------A..........B........C<BR>\n" );
document.write( "row 1.............2..........4........3<BR>\n" );
document.write( "row 2.............3..........5........1<BR>\n" );
document.write( "row 3.............4..........2........5<BR>\n" );
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document.write( "Ho: Horses and lanes are independent<BR>\n" );
document.write( "Ha: They are dependent<BR>\n" );
document.write( "Run a Chi-Sq on the 3 x 3 Matrix and get the following<BR>\n" );
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document.write( "Test Statistic: Chi-Sq = 0.213447...<BR>\n" );
document.write( "p-value = 0.37789..<BR>\n" );
document.write( "df=4<BR>\n" );
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document.write( "Conclusion: Since p-value is greater than 5%, Fail to reject Ho.<BR>\n" );
document.write( "Horses and lanes are independent.<BR>\n" );
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document.write( "Hope that helps.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H. </SPAN>\n" );
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