Errors and Power Practice

Question

Question 1 (1 point)

A medical doctor uses a diagnostic test to determine whether a patient has arthritis. A treatment will be prescribed only if the doctor thinks the patient has arthritis. The situation is similar to using a null and an alternative hypothesis to decide whether to prescribe the treatment. The hypotheses might be stated as follows.

H0 : The patient does not have arthritis

Ha : The patient has arthritis

Which of the following represents a Type II error for the hypotheses?

a	Failing to diagnose arthritis in a patient who does not have arthritis
b	Prescribing treatment to a patient regardless of the diagnosis
c	Diagnosing arthritis in a patient who has arthritis
d	Failing to diagnose arthritis in a patient who has arthritis
e	Diagnosing arthritis in a patient who does not have arthritis

Question 2 (1 point)

A one-sided hypothesis test is to be performed with a significance level of 0.05. Suppose that the null hypothesis is false. If a significance level of 0.01 were to be used instead of a significance level of 0.05, which of the following would be true?

a	Neither the probability of a Type II error nor the power of the test would change.
b	Both the probability of a Type II error and the power of the test would decrease.
c	Both the probability of a Type II error and the power of the test would increase.
d	The probability of a Type II error would decrease and the power of the test would increase.
e	The probability of a Type II error would increase and the power of the test would decrease.

Question 3 (1 point)

Which of the following gives the probability of making a Type I error?

a	the significance level
b	the sample size
c	the power
d	the p-value
e	the standard error

Question 4 (1 point)

Consider the results of a hypothesis test, which indicate there is not enough evidence to reject the null hypothesis. Which of the following statements about error is correct?

a	Both types of error could have been made, but the probability of a Type I error is less than the probability of a Type II error.
b	A Type I error could have been made, but not a Type II error.
c	Both types of error could have been made, but the probability of a Type I error is greater than the probability of a Type II error.
d	A Type II error could have been made, but not a Type I error.
e	The type of error that could have been made is not possible to determine without knowing the statement of the null hypothesis.

Answer 1

A Type II error occurs when you fail to reject the null hypothesis when it is false. Failing to diagnose arthritis in a patient who has arthritis would be a Type I error (d)

If you decrease the level of significance the probability of a Type II error would increase and thus the power would decrease as the level of significance and the probability of a Type II error are inversely related. (e)

The probability of making a Type I error and the significance level are the same value (a).

A Type I error can only occur if you reject the null hypothesis when it is true. Here we have failed to reject the null hypothesis so a Type I error cannot have been made. You cannot make a Type I and Type II errors at the same time. So a Type II error could have been made but not a Type I error. (d)