document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=126318>Question 126318</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The following table shows gender and soda preference of 300 people sampled:	<BR>\n" );
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document.write( "Soda Preference<BR>\n" );
document.write( "Gender	Diet Soda	Regular Soda	No Soda	Totals<BR>\n" );
document.write( "Male	70	               40	20	130<BR>\n" );
document.write( "Female	110	               45	15	170<BR>\n" );
document.write( "Total	180	               85	35	300<BR>\n" );
document.write( "A.	Draw a Bayesian Tree from the data in the table.<BR>\n" );
document.write( "B.	Are these two variables (gender & soda preference) independent?  <BR>\n" );
document.write( "C.	What is the probability of randomly selecting someone who is Male or prefers Regular Soda?<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 #92596 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=92596\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Soda Preference<BR>\n" );
document.write( "Gender Diet Soda Regular Soda No Soda Totals<BR>\n" );
document.write( "Male 70 40 20 130<BR>\n" );
document.write( "Female 110 45 15 170<BR>\n" );
document.write( "Total 180 85 35 300<BR>\n" );
document.write( "A. Draw a Bayesian Tree from the data in the table.<BR>\n" );
document.write( "The tree has two roots: Male and Female<BR>\n" );
document.write( "Each root as three brances: Diet, Regular, None<BR>\n" );
document.write( "Read the probabilities of the branches from the data<BR>\n" );
document.write( "For example the branch Male-Diet has probability (70/130)= 7/13<BR>\n" );
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document.write( "B. Are these two variables (gender & soda preference) independent?<BR>\n" );
document.write( "Ho: The rows are independent<BR>\n" );
document.write( "Ha: The rows are dependent<BR>\n" );
document.write( "Chi-square Test:<BR>\n" );
document.write( "Chi-Square = 29.179441<BR>\n" );
document.write( "p-value = 4.61x10^-7 or extremely small<BR>\n" );
document.write( "Conclusion: Fail to reject Ho<BR>\n" );
document.write( "The gender and soda preference are independent.<BR>\n" );
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document.write( "C. What is the probability of randomly selecting someone who is Male or prefers Regular Soda?<BR>\n" );
document.write( "P(Male or prefers Regular) = P(M)+P(R)-P(M and R)<BR>\n" );
document.write( "= 130/300 + 85/300 - 40/300 = 175/300<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.\r<BR>\n" );
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