Question
In: Statistics and Probability
A total of 5101 people who worked at a chemical factory were followed from 1950 to...
A total of 5101 people who worked at a chemical factory were followed from 1950 to 1990 and monitored for kidney cancer. Of 3500 workers working with solvents, 17 develop kidney cancer. Of 1601 of the workers, which are not exposed to solvents, 8 develop kidney cancer. Is there an association between exposure to solvent use and kidney cancer?
Solutions
Expert Solution
The data can be summarised in the following table
| Kidney Cancer | No Kidney Cancer | Total | |
| Exposed to solvent | 17 | 3483 | 3500 |
| Not exposed to solvent | 8 | 1593 | 1601 |
| Total | 25 | 5076 | 5101 |
In order to test whether there is an association between exposure to solvent use and kidney cancer, we first need to determine the hypothesis.
The Null Hypothesis is
H0: Exposure to solvent use and Kidney Cancer are independent.
Ha: Exposure to solvent use and Kidney Cancer are associated.
The expected value for each of the categories in the table is given by
where 
is the row sum and 
is the column sum. n is the total number of workers.
The expected value table is
| Kidney Cancer | No Kidney Cancer | Total | |
| Exposed to solvent | 17.153 | 3482.847 | 3500 |
| Not exposed to solvent | 7.847 | 1593.153 | 1601 |
| Total | 25 | 5076 | 5101 |
The value of the chi-squared test statistics is
The degree of freedom is
= (r-1) * (c-1)
= (2-1) * (2-1) = 1
The p-value corresponding to a chi-square statistics of 0.00436 and a degree of freedom is 0.947.
The p-value is very high which means there is a probability of 0.947 that the null hypothesis is correct.
Hence, we would accept the null hypothesis.
Conclusion: There is no association between exposure to solvent use and kidney cancer.
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