Question

5. 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. 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.” (1 points for each)   

1. 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 have considered the null and alternative hypotheses below:

H₀: p = value for areas without nuclear facilities

H_a: p > value for areas without nuclear facilities

According to the spokesperson’s statement, what is the conclusion of the National Cancer Institute? Select one of the following:

Reject H₀                          Fail to reject H₀                                         Reject H_a                          Fail to reject H_a

2. If the National 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? Read carefully and select one of the following:

1. A Type II error, if the researchers were incorrect in their conclusion this would be rejecting the null hypothesis when the null hypothesis is true.
2. 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.
3. 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 false.
4. 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.

Answer 1

1. The spoke person said that : "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."

So according to the spoke person the conclusion is

FAIL TO REJECT .

2. Here we accept . So there is no possibility of type 1 error as the type 1 error is made rejecting the null hypothesis given that null hypothesis is true. So we can cancel option 2 and 4.

Type 2 error is caused when accepting when really is true. So in this case the answer is :

3)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 false.