document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=132971>Question 132971</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Please help. Found the question but the calculations were not available. Thank you in advance. 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 alpha=.05, is the correctness of the prediction different for the two types of cola drinker? Could you identify your favorite brand in this kind of test? Since it is a 2x2 table, try also a two taled two sample z test for &#1087;1= &#1087;2 and verify that z2 is the same as your chi-square statistic. Which test do you prefer? Why? <BR>\n" );
document.write( "Show how the degrees of freedom are calculated, find the critical value of chi-square, and interpret the p-value. Is the conclusion sensitive to the level of significance chosen?<BR>\n" );
document.write( "Correct? Regular Cola	Diet Cola	Row Total<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( "Col total--------       19	27	46<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 #97226 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=97226\">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.<BR>\n" );
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document.write( " Correct?............ Reg Cola Diet Cola	Row Total<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( "Col total--------       19	27	   46<BR>\n" );
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document.write( "Research question: at alpha=.05, <BR>\n" );
document.write( "Is the correctness of the prediction different for the two types of cola drinker? <BR>\n" );
document.write( "Ho: They are the same<BR>\n" );
document.write( "Ha: They are different<BR>\n" );
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document.write( "un a Chi-Sq. Test on the 2X2 data:<BR>\n" );
document.write( "Reg Cola: 7....12<BR>\n" );
document.write( "DietCola: 7....20<BR>\n" );
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document.write( "Test statistic: Chi-Sq = 0.62768...<BR>\n" );
document.write( "p-value = 0.428207...<BR>\n" );
document.write( "Show how the degrees of freedom are calculated, <BR>\n" );
document.write( "df= (# of rows -1)(# of columns) = 1*1 = 1<BR>\n" );
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document.write( "Find the critical value of chi-square for alpha = 5% and df=1,<BR>\n" );
document.write( "Left margin = 0.001; Right margin is 7.879<BR>\n" );
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document.write( "Interpret the p-value.<BR>\n" );
document.write( "At least 43.8% of test results could provide stronger evidence for<BR>\n" );
document.write( "rejecting Ho.<BR>\n" );
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document.write( "Since p-value is greater then alpha = 5%, Fail to Reject Ho.<BR>\n" );
document.write( "Conclusion: Correctness of the predictions of RegCola and DietCola drinkers is not different.<BR>\n" );
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document.write( "Could you identify your favorite brand in this kind of test?<BR>\n" );
document.write( "Probably not since this test group was wrong in their identification<BR>\n" );
document.write( "32 out of 46 times.<BR>\n" );
document.write( "--------------------- <BR>\n" );
document.write( "Since it is a 2x2 table, try also a two tailed two sample z test for p1= p2 and verify that z2 is the same as your chi-square statistic.<BR>\n" );
document.write( "Ho: p1-p2=0<BR>\n" );
document.write( "Ha: p1-p2 is not 0<BR>\n" );
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document.write( "Critical Value for 2-tail 2-proportion z test with alpha=5%: z = +/-1.96<BR>\n" );
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document.write( "If data is pooled p-bar = (x1+x2)/(n1+n2) =14/46 = 0.304<BR>\n" );
document.write( "Test statistic:<BR>\n" );
document.write( "z(7/19 - 7/27) =  0.10916/sqrt[(0.304*0.696/19) + (0.304*0.696/27)]<BR>\n" );
document.write( "= 0.10916/sqrt(0.01897) = 0.015056...<BR>\n" );
document.write( "-----------------------------------<BR>\n" );
document.write( "Conclusion: Since the test statistic is between -1.96 and +1.96, Fail to Reject Ho.<BR>\n" );
document.write( "The proportions are the same.<BR>\n" );
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document.write( "Show how the degrees of freedom are calculated, <BR>\n" );
document.write( "df= (# of rows -1)(# of columns) = 1*1 = 1<BR>\n" );
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document.write( "Find the critical value of chi-square,<BR>\n" );
document.write( "Left margin = 0.001; Right margin is 7.879<BR>\n" );
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document.write( "p-value for the test statistic = 2P(z > 0.015056...) = 98.8%<BR>\n" );
document.write( "Interpret the p-value: 98.8% of the test results could have <BR>\n" );
document.write( "provided stronger evidence to reject Ho..<BR>\n" );
document.write( "Is the conclusion sensitive to the level of significance chosen?<BR>\n" );
document.write( "Not when the p-value is as large as 98.9%<BR>\n" );
document.write( "-----------------<BR>\n" );
document.write( "Which test do you prefer? Why?<BR>\n" );
document.write( "The Chi-Sq is much easier to run and interpret.<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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