Ok, so i\'m studying the null hypothesis, and the second part to this question i

Question

Ok, so i'm studying the null hypothesis, and the second part to this question is making me pull my hair out. MY WEBASSIGN SAYS THE ANSWER IS D.) WHEN I THINK IT IS A.)

Can someone confirm if this is a mistake or if it is really D.) and why?

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. 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 below.

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?

A.)The researchers rejected H0.

B.) The researchers failed 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.

[A]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.

[B]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.

[C]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.

[D]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.

Explanation / Answer

Given that,

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. 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 below.

H0: p = value for areas without nuclear facilities

Ha: p > value for areas without nuclear facilities

From the given information fail to reject H0 at 5% level of significance.

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.

This statement means that we accept null when alternative is true.

Type II error occure.

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