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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