High School

The mortality experience of 8,146 male employees of a research, engineering, and metal-fabrication plant in Tonawanda, New York, was studied from 1946 to 1981. Potential workplace exposures included welding fumes, cutting oils, asbestos, organic solvents, and environmental ionizing radiation, as a result of waste disposal during the Manhattan Project of World War II. Comparisons were made for specific causes of death between mortality rates in workers and U.S. white-male mortality rates from 1950 to 1978.

Suppose that 17 deaths from cirrhosis of the liver were observed among workers who were hired prior to 1946 and who had worked in the plant for 10 or more years, whereas 6.3 were expected based on U.S. white-male mortality rates.

Perform a significance test to assess whether there is an association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945. Report a p-value.

Answer :

Final Answer:

The significance test for assessing the association between mortality from cirrhosis of the liver and duration of employment yielded a p-value of approximately 0.0019.

Explanation:

To perform the significance test, we can use the chi-squared test for independence. First, we calculate the expected number of deaths from cirrhosis of the liver based on U.S. white-male mortality rates for workers hired after 1945. Then, we compare these expected values to the observed number of deaths among workers who were hired after 1945 and had worked in the plant for 10 or more years. The chi-squared statistic is calculated using the formula [tex]\(\chi^2 = \sum \frac{(O - E)^2}{E}\)[/tex], where O is the observed frequency and E is the expected frequency. Finally, we use the chi-squared statistic to find the p-value from the chi-squared distribution with appropriate degrees of freedom.

Given that 17 deaths were observed among workers hired after 1945, and the expected number of deaths based on U.S. white-male mortality rates was 6.3, we calculate the chi-squared statistic as [tex]\(\chi^2 = \frac{(17 - 6.3)^2}{6.3} = 13.74\)[/tex]. Using the chi-squared distribution table or statistical software, we find the p-value associated with this chi-squared statistic, which is approximately 0.0019. Since the p-value is less than the conventional significance level of 0.05, we reject the null hypothesis of independence. Therefore, there is a significant association between mortality from cirrhosis of the liver and duration of employment in the group hired after 1945.

This analysis provides evidence suggesting that employment duration in the group hired after 1945 is associated with an increased risk of mortality from cirrhosis of the liver. The study underscores the importance of considering workplace exposures and their potential health effects, particularly in industries with known hazardous materials or processes. By conducting significance tests and analyzing mortality data, researchers and policymakers can identify and address occupational health risks to protect workers' well-being.

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