Question 1

Suppose environmentalists test whether high-frequency radio transmissions increase bird hatchling mortality near cell towers. They use a significance level of $$\alpha = 0.05$$ and fail to reject the null hypothesis. What does this imply about the P-value, and what can you conclude if $$\alpha is $$changed to $$0.01$$?

Accepted Answer

The P-value is greater than 0.05; they would also fail to reject the null hypothesis at $$\alpha = 0.01.$$

Question 2

In the context of hypothesis testing for Alzheimer’s disease, what is the null hypothesis ($$H_0) $$and the alternative hypothesis ($$H_A$$)?

Accepted Answer

$$H_0$$: The person is healthy. $$H_A$$: The person has Alzheimer’s disease.

Question 3

A Type I error in the Alzheimer’s test context means:

Accepted Answer

A healthy person is incorrectly diagnosed as having Alzheimer’s disease.

Question 4

A Type II error in the Alzheimer’s test context means:

Accepted Answer

A person with Alzheimer’s disease is incorrectly diagnosed as healthy.

Question 5

Given a false positive rate of 4% and a false negative rate of 8% for the Alzheimer’s test, what is the power of the test?

Accepted Answer

$$0.92$$

Question 6

A company wants to prove that more than 20% of city residents recognize their product after hearing a radio ad. What are the correct null and alternative hypotheses?

Accepted Answer

$$H_0$$: p = 0.20$$, H_A$$: p \u003e 0.20$$

Question 7

If the company lowers the significance level from $$\alpha = 0.10 to$$ $$\alpha = 0.05$$, what happens to the probability of a Type I error?

Accepted Answer

It decreases.

Question 8

What does the power of a statistical test represent in the context of the advertising survey?

Accepted Answer

The probability of correctly concluding that more than 20% of residents recognize the product when it is true.

Question 9

For which significance level will the power of the test be higher: $$\alpha = 0.10 or$$ $$\alpha = 0.05$$? Why?

Accepted Answer

$$\alpha = 0.10$$, because there is a greater chance of rejecting the null hypothesis.

Question 10

If the radio station increases the sample size from 400 to 600, what happens to the risk of a Type II error?

Accepted Answer

It decreases.

Question 11

Which is generally considered more serious in medical testing: a Type I or Type II error, and why?

Accepted Answer

Type II error, because it means a sick person may not receive needed treatment.

Question 12

If a hypothesis test fails to reject the null hypothesis at $$\alpha = 0.05$$, what can you conclude about the P-value?

Accepted Answer

The P-value is greater than 0.05.

Question 13

If the P-value for a test is greater than 0.05 but less than 0.10, what is the correct decision at $$\alpha = 0.10$$?

Accepted Answer

Reject the null hypothesis.

Question 14

Which of the following best describes a false negative in the context of Alzheimer’s disease testing?

Accepted Answer

A person with Alzheimer’s disease is diagnosed as healthy.

Question 15

If the significance level $$\alpha is $$increased, what happens to the probability of a Type I error?

Accepted Answer

It increases.

Hypothesis Testing, Significance Levels, and Errors in Statistics

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