10.21 The National Cancer Institute conducted a 2-year study to determine whether cancer death rates for areas near nuclear power plants are higher than for areas without nuclear facilities (San Luis Obispo Telegram-Tribune, September 17, 1990). A spokesperson for the Cancer Institute said, “From the data at hand, there was no convincing evidence of any increased risk of death from any of the cancers surveyed due to living near nuclear facilities. However, no study can prove the absence of an effect.”

a. Let p denote the proportion of the population in areas near nuclear power plants who die of cancer during a given year. The researchers at the Cancer Institute might have considered the two rival hypotheses of the form H0: p  value for areas without nuclear facilities Ha: p  value for areas without nuclear facilities Did the researchers reject H0 or fail to reject H0?

b. If the Cancer Institute researchers were incorrect in their conclusion that there is no increased cancer risk associated with living near a nuclear power plant, are they making a Type I or a Type II error?

Explain.

c. Comment on the spokesperson’s last statement that no study can prove the absence of an effect. Do you agree with this statement?