To weaken the hospital spokesperson's argument that the chemical test would have little impact on the breast cancer death rate because virtually all breast tumors are detectable by self-examination, we need to find information that suggests the chemical test would still be valuable. Let's evaluate the options:
A. This option weakens the spokesperson's argument by stating that fatal breast tumors are often not revealed by self-examination until it's too late for effective treatment. This suggests that relying solely on self-examination might not be sufficient in detecting all breast tumors early.B. This option doesn't directly address the argument made by the spokesperson. It discusses the stage of development of breast tumors compared to lung tumors but doesn't provide relevant information about the impact of the chemical test.
C. This option suggests that mammograms, another form of breast cancer testing, are already widely used and less expensive than the chemical test. While it provides some context, it doesn't directly weaken the argument.
D. This option states that the new test would benefit only half of the population (women). However, it doesn't address the effectiveness of the test in detecting breast tumors, which is the central point of the spokesperson's argument.
E. This option is not relevant to the effectiveness of the chemical test in detecting breast tumors and therefore doesn't weaken the spokesperson's argument.
Option A is the most relevant to weakening the spokesperson's argument because it suggests that self-examination may not be sufficient to detect all breast tumors early, and some fatal tumors might not be revealed until it's too late for effective treatment. This implies that an additional test like the chemical test could still have a significant impact on the breast cancer death rate.