Question
In: Math
The following data represent the level of health and the level of education for a random...
The following data represent the level of health and the level of
education for a random sample of 1630 residents.
Excellent Good Fair Poor
Not a H.S. graduate 114 184 106 126
H.S. graduate 75 120 82 94
Some college 110 154 102 107
Bachelor Degree or higher 121 156 85 133
A. Calculate the Chi Square test statistic (Round to three decimal places)
B. Give the P Value (Round to three decimal places)
C. Make a proper conclusion
Reject Ho. There is sufficient evidence that education and health are dependent.
Fail to reject Ho. There is sufficient evidence that education and health are dependent.
Reject Ho. There is not sufficient evidence that education and health are dependent.
Fail to reject Ho. There is not sufficient evidence that education and health are dependent.
Solutions
Expert Solution
The null and alternative hypothesis is
H0: Education and health are independent.
H1: Education and health are dependent.
Level of significance = 0.05
Test statistic is
O: Observed frequency
E: Expected frequency.
E = ( Row total*Column total) / Grand total
| Excellent | Good | Fair | Poor | Total | |
| Not a H.S. graduate | 114 | 184 | 106 | 126 | 530 |
| H.S. graduate | 75 | 120 | 82 | 94 | 371 |
| Some college | 110 | 154 | 102 | 107 | 473 |
| Bachelor | 121 | 156 | 85 | 133 | 495 |
| Total | 420 | 614 | 375 | 460 | 1869 |
| O | E | (O-E) | (O-E)^2 | (O-E)^2/E |
| 114 | 119.1011 | -5.10112 | 26.02146 | 0.218482 |
| 184 | 174.1145 | 9.8855 | 97.72312 | 0.561258 |
| 106 | 106.3403 | -0.34029 | 0.115797 | 0.001089 |
| 126 | 130.4441 | -4.44409 | 19.74992 | 0.151405 |
| 75 | 83.37079 | -8.37079 | 70.07007 | 0.840463 |
| 120 | 121.8801 | -1.88015 | 3.534963 | 0.029004 |
| 82 | 74.4382 | 7.561798 | 57.18079 | 0.768165 |
| 94 | 91.31086 | 2.689139 | 7.231466 | 0.079196 |
| 110 | 106.2921 | 3.707865 | 13.74826 | 0.129344 |
| 154 | 155.389 | -1.38898 | 1.92926 | 0.012416 |
| 102 | 94.90369 | 7.096308 | 50.35759 | 0.530618 |
| 107 | 116.4152 | -9.4152 | 88.6459 | 0.761463 |
| 121 | 111.236 | 9.764045 | 95.33657 | 0.857066 |
| 156 | 162.6164 | -6.61637 | 43.77638 | 0.2692 |
| 85 | 99.31782 | -14.3178 | 204.9999 | 2.06408 |
| 133 | 121.8299 | 11.17014 | 124.7721 | 1.024151 |
| Total | 8.30 |
A.
B. Degrees of freedom = 16 - 1 = 15
P-value = P(
) = 0.9113
c) P-value >0.05 we fail to reject null hypothesis.
Fail to reject Ho. There is not sufficient evidence that education and health are dependent.
milcah answered 4 months agoRelated Solutions
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