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? Observed Sample of 800 People Cola A Cola B Cola C Total 15-29 94 102 105 301 30-44 99 97 86 282 45-59 68 73 76 217 Total 261 272 267 800 Expected Values Cola A Cola B Cola C Total 15-29 (301)(261)/800 (301)(272)/800 (301)(267)/800 301 30-44 (282)(261)/800 (282)(272)/800 (282)(267)/800 282 45-59 (217)(261)/800 (217)(272)/800 (217)(267)/800 217 Total 261 272 267 800 Ho: Cola preference and age are independent (no association) Ha: Cola preference and age are dependent (there is an association) Degrees of freedom = (3-1)(3-1) = 2(2) = 4 (Row - 1)(Column - 1) Test Statistic: x2: = + + + + ( )2 (94 98.201)2 98.201 (102 102.342) 102.34 (105 100.46)2 100.46 (99 92.003)2 92.003 (97 95.88)2 95.88 + + + + = 1.927 (86 94.118)2 94.118 (68 70.796)2 70.796 (73 73.78)2 73.78 (76 72.424)2 72.424 Critical Value: x2 From table at 0.005 = 14.860 p-value: 0.7492 0.7492 > .005 Fail to Reject Conclusion: At the 0.005 level of significance, the evidence does not support the claim that an association exists between cola preference and age