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 dependent (there is an association) Ha: Cola preference and age are independent (no association) Degrees of freedom (3-1)(3-1)=2(2)=4 (Row 1)(Column - 1) Test Statistic: x2: (0-e)² (86-94.118)2 94.118 (94-98.201) (102-102.342) (105-100.46)2(99-92.003)² (97-95.88)² + + + 98.201 102.34 100.46 92.003 95.88 + 73.78 (68-70.796)2 (73-73.78)2 (76-72.424)² 70.796 + 1.927 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 support the claim that an association exists between cola preference and age.
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 dependent (there is an association) Ha: Cola preference and age are independent (no association) Degrees of freedom (3-1)(3-1)=2(2)=4 (Row 1)(Column - 1) Test Statistic: x2: (0-e)² (86-94.118)2 94.118 (94-98.201) (102-102.342) (105-100.46)2(99-92.003)² (97-95.88)² + + + 98.201 102.34 100.46 92.003 95.88 + 73.78 (68-70.796)2 (73-73.78)2 (76-72.424)² 70.796 + 1.927 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 support the claim that an association exists between cola preference and age.
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Hypothesis Testing Review - Error Analysis
Transcribed Image Text: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 dependent (there is an association)
Ha: Cola preference and age are independent (no association)
Degrees of freedom (3-1)(3-1)=2(2)=4
(Row 1)(Column - 1)
Test Statistic: x2: (0-e)²
(86-94.118)2
94.118
(94-98.201) (102-102.342) (105-100.46)2(99-92.003)² (97-95.88)²
+
+
+
98.201
102.34
100.46
92.003
95.88
+
73.78
(68-70.796)2 (73-73.78)2 (76-72.424)²
70.796
+
1.927
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 support the claim that an
association exists between cola preference and age.
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