The paper "Living Near Nuclear Power Plants and Thyroid Cancer Risks"† investigated whether living near a nuclear power plant increases the risk of thyroid cancer. The authors of this paper concluded...

The paper "Living Near Nuclear Power Plants and Thyroid Cancer Risks"† investigated whether living near a nuclear power plant increases the risk of thyroid cancer. The authors of this paper concluded that there was no evidence of increased risk of thyroid cancer in areas that were near a nuclear power plant.

(a)

Let p denote the proportion of the population in areas near nuclear power plants who are diagnosed with thyroid cancer during a given year. The researchers who wrote this paper might have considered the two rival hypotheses of the form below.

H0: p is equal to the corresponding value for areas without nuclear power plants

Ha: p is greater than the corresponding value for areas without nuclear power plants

Did the researchers reject

H0
or fail to reject

H0?
The researchers rejected H0.

The researchers failed to reject H0.

(b)

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

A Type II error, if the researchers were incorrect in their conclusion this would be rejecting the null hypothesis when the null hypothesis is false.

A Type I error, if the researchers were incorrect in their conclusion this would be rejecting the null hypothesis when the null hypothesis is false.

A Type I error, if the researchers were incorrect in their conclusion this would be failing to reject the null hypothesis when the null hypothesis is true.

A Type II error, if the researchers were incorrect in their conclusion this would be failing to reject the null hypothesis when the null hypothesis is true.

(c)

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

Yes, the study did not provide convincing evidence that there is a higher cancer death rate for people who live close to nuclear facilities, but it doesn't mean there was no such effect.

No, just because the study couldn't provide convincing evidence doesn't mean it is impossible.