Question

Suppose that 28 cancer deaths are noted among workers exposed to asbestos in a building materials plant from 1981 to 1985. Only 20.5 cancer deaths are expected from statewide mortality rates. Suppose that we want to know if there is a significant excess of cancer deaths among these workers. What is the null hypothesis? Is a one- or two-sided test appropriate here?

Answer 1

Suppose, random variable X denotes number of cancer deaths among workers exposed to asbestos in a building materials plant from 1981 to 1985.

We want to know if there is a significant excess of cancer deaths among these workers. To do so, we assume that number of cancer deaths is 20.5 as null hypothesis and as alternative hypothesis we have to check whether observed number is significantly higher or not.

Thus we have to test for null hypothesis

against the alternative hypothesis

Clearly, this is a one sided test (more specifically right sided test).