The following table is from the publication of Vital and Health Statistics from
ID: 3152486 • Letter: T
Question
The following table is from the publication of Vital and Health Statistics from the Centers for Disease Control and Prevention/National Center for Health Statistics. The individuals in the following table have an eye irritation, a nose irritation, or a throat irritation. They have only one of the three. Is there sufficient evidence to reject the hypothesis that the type of ear, nose, or throat irritation is independent of the age group at a level of significance equal to .05? Age (years) Type of Irritation 18-29 30-44 45-64 65 and Older Eye 429 582 356 58 Nose 921 1328 772 97 Throat 244 329 159 19 (a) Find the test statistic. (Give your answer correct to two decimal places.) (ii) Find the p-value. (Give your answer bounds exactly.) < p <
Explanation / Answer
The following table is from the publication of Vital and Health Statistics from the Centers for Disease Control and Prevention/National Center for Health Statistics. The individuals in the following table have an eye irritation, a nose irritation, or a throat irritation. They have only one of the three. Is there sufficient evidence to reject the hypothesis that the type of ear, nose, or throat irritation is independent of the age group at a level of significance equal to .05? Age (years) Type of Irritation 18-29 30-44 45-64 65 and Older Eye 429 582 356 58 Nose 921 1328 772 97 Throat 244 329 159 19
(a) Find the test statistic. 8.75 (Give your answer correct to two decimal places.)
Chi-Square Test
Observed Frequencies
Age
18-29
30-44
45-64
65 and older
Total
Eye
429
582
356
58
1425
Nose
921
1328
772
97
3118
Throat
224
329
159
19
731
Total
1574
2239
1287
174
5274
Expected Frequencies
Age
18-29
30-44
45-64
65 and older
Total
Eye
425.28
604.96
347.74
47.01
1425
Nose
930.55
1323.70
760.88
102.87
3118
Throat
218.16
310.34
178.38
24.12
731
Total
1574
2239
1287
174
5274
Calculations
fo-fe
3.7156
-22.9630
8.2611
10.9863
-9.5521
4.2984
11.1229
-5.8692
5.8366
18.6646
-19.3840
-5.1172
(fo-fe)^2/fe
0.0325
0.8716
0.1963
2.5673
0.0981
0.0140
0.1626
0.3349
0.1561
1.1225
2.1063
1.0858
Data
Level of Significance
0.05
Number of Rows
3
Number of Columns
4
Degrees of Freedom
6
Results
Critical Value
12.592
Chi-Square Test Statistic
8.747953
p-Value
0.1883
(ii) Find the p-value. P=0.1883 (Give your answer bounds exactly.)
0.1 < p < 0.2
Chi-Square Test
Observed Frequencies
Age
18-29
30-44
45-64
65 and older
Total
Eye
429
582
356
58
1425
Nose
921
1328
772
97
3118
Throat
224
329
159
19
731
Total
1574
2239
1287
174
5274
Expected Frequencies
Age
18-29
30-44
45-64
65 and older
Total
Eye
425.28
604.96
347.74
47.01
1425
Nose
930.55
1323.70
760.88
102.87
3118
Throat
218.16
310.34
178.38
24.12
731
Total
1574
2239
1287
174
5274
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