Question

9. A soft drink company is interested in knowing whether there is a relationship between cola preference and age. A random sample of 800 people is chosen for a taste test. The results of the study are found in the following table. Is there sufficient evidence at the 0.005 level of significance to lead you to believe that there is an association between cola preference and age? *You can use your test value or the p-value to decide. Cola A Cola B Cola C 15-29 94 102 105 30-44 99 97 86 45-59 68 73 76 State the Hyp: Test Value is_____=______ P-value = ________ Decision:__________________________________________________ Conclusion:_______________________________________

Answer 1

Ho: given two variable are independent

H1: Given two variables are not independent

	Observed Frequencies
	0
0	15-29	30-44	45-59				Total
cola A	94	99	68				261
cola B	102	97	73				272
cola C	105	86	76				267
Total	301	282	217				800
	Expected frequency of a cell = sum of row*sum of column / total sum
	Expected Frequencies
	15-29	30-44	45-59				Total
cola A	301*261/800=98.201	282*261/800=92.003	217*261/800=70.796				261
cola B	301*272/800=102.34	282*272/800=95.88	217*272/800=73.78				272
cola C	301*267/800=100.459	282*267/800=94.118	217*267/800=72.424				267
Total	301	282	217				800
	(fo-fe)^2/fe
cola A	0.180	0.532	0.110
cola B	0.001	0.013	0.008
cola C	0.2053	0.7001	0.1766

Chi-Square Test Statistic,χ² = Σ(fo-fe)^2/fe =   1.927          
              
Level of Significance =   0.005          
Number of Rows =   3          
Number of Columns =   3          
Degrees of Freedom=(#row - 1)(#column -1) = (3- 1 ) * ( 3- 1 ) =   4          
              
p-Value =   0.7492   [Excel function: =CHISQ.DIST.RT(χ²,df) ]     
Decision:    p value > α , do not reject Ho         
there is not an association between cola preference and age

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