document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=131000>Question 131000</A>This question is from textbook <A HREF=http://www.amazon.com/exec/obidos/ASIN/0073215759/algebrahomeworkh>Applied Statistics in Business and Economics</A><BR>\n" );
document.write( ": <I><SPAN STYLE=\"word-break: break-all;\"> Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At &#945; = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample<BR>\n" );
document.write( "z test for &#960;1 = &#960;2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why?<BR>\n" );
document.write( "Yes got it right - 7, 7, 14<BR>\n" );
document.write( "no got it wrong - 12, 20, 32<BR>\n" );
document.write( "total - 19, 27, 46 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #95746 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=95746\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Can people really identify their favorite brand of cola? Volunteers tasted Coca-Cola Classic, Pepsi, Diet Coke, and Diet Pepsi, with the results shown below. Research question: At &#945; = .05, is the correctness of the prediction different for the two types of cola drinkers? Could you identify your favorite brand in this kind of test? Since it is a 2 × 2 table, try also a two-tailed two-sample<BR>\n" );
document.write( "z test for &#960;1 = &#960;2 (see Chapter 10) and verify that z2 is the same as your chi-square statistic.Which test do you prefer? Why?<BR>\n" );
document.write( "Yes got it right - 7, 7, 14<BR>\n" );
document.write( "no got it wrong - 12, 20, 32<BR>\n" );
document.write( "total - 19, 27, 46<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Chi-Sq Test:<BR>\n" );
document.write( "Ho: the columns are homogeneous<BR>\n" );
document.write( "Ha; the columns are not homogeneous<BR>\n" );
document.write( "Using a TI-calculator Chi-Sq Test I get:<BR>\n" );
document.write( "Test statistic: Chi-Sq = 0.62768....<BR>\n" );
document.write( "p-value = 0.428..<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Conclusion: Reject Ho; <BR>\n" );
document.write( "The columns are not homogeneous<BR>\n" );
document.write( "=======================================<BR>\n" );
document.write( "Two-tailed sample z test:<BR>\n" );
document.write( "Ho: mu1 = mu2<BR>\n" );
document.write( "Ha: mu1 is not equal to mu2<BR>\n" );
document.write( "Critical value for 2-tailed test and alpha=5%: +-1.96<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "x1-bar = 19/2= 9.5<BR>\n" );
document.write( "x2-bar = 27/2= 13.5<BR>\n" );
document.write( "sigma1^2 =7.77817^2 = 60.5<BR>\n" );
document.write( "n1=19<BR>\n" );
document.write( "sigma2^2 =9.1924^2=84.5<BR>\n" );
document.write( "n2=27<BR>\n" );
document.write( "---------------<BR>\n" );
document.write( "z(9.5-13.5)/sqrt[(60.5/19) + (84.5)/27] = -1.59<BR>\n" );
document.write( "p-value = 2P(-10 < z <-1.59) = 0.1118...<BR>\n" );
document.write( "--------<BR>\n" );
document.write( "Conclusion: Since p-value > alpha, Fail to Reject Ho.<BR>\n" );
document.write( "The columns are homogeneous.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "As you see, the test results are not the same.<BR>\n" );
document.write( "I'll leave the discussion of the final questions to you.<BR>\n" );
document.write( "-----------------------------<BR>\n" );
document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );