Home / AP® Exam / AP® Statistics / 6.7 Potential Errors When Performing Tests- MCQs

AP Statistics 6.7 Potential Errors When Performing Tests- MCQs - Exam Style Questions

AP Statistics -MCQs and Answers - All Topics

Question

A statistical test involves the following null and alternative hypotheses.
\(H_0:\ \mu=64\)
\(H_a:\ \mu>64\)
Which of the following describes a Type II error?
(A) Failing to reject the null hypothesis when the population mean is \(64\)
(B) Failing to reject the null hypothesis when the population mean is greater than \(64\)
(C) Rejecting the null hypothesis when the population mean is \(64\)
(D) Rejecting the null hypothesis when the population mean is greater than \(64\)
(E) Failing to reject the null hypothesis when the \(p\)-value is less than the significance level
▶️ Answer/Explanation
Detailed solution

Type II error \(= \beta\): fail to reject \(H_0\) even though \(H_a\) is true.
Here \(H_a:\mu>64\). So a Type II error occurs when we do not reject \(H_0\) but in reality \(\mu>64\).
✅ Answer: (B)

Question

A doctor uses a new diagnostic test to indicate whether a patient has a certain disease. The doctor will prescribe medication for the patient if the doctor believes the patient has the disease, as indicated by the diagnostic test. The situation is similar to using a null hypothesis and an alternative hypothesis to decide whether to prescribe the medication. The hypotheses can be stated as follows.
$H_{0}$: The patient does not have the disease.
$H_{a}$: The patient has the disease.
Which of the following best describes the power of the test?
(A) The probability that the new test is better than an older test to indicate whether a patient has the disease
(B) The probability that the new test indicates the disease in a patient who has the disease
(C) The probability that the new test indicates the disease in a patient who does not have the disease
(D) The probability that the new test does not indicate the disease in a patient who has the disease
(E) The probability that the new test does not indicate the disease in a patient who does not have the disease
▶️ Answer/Explanation
Detailed solution

1. Define Power in Hypothesis Testing:
The power of a test is the probability of correctly rejecting a false null hypothesis ($H_0$).
Power = $P(\text{Reject } H_0 \text{ | } H_0 \text{ is false})$

2. Translate the Terms to the Context:
– “Reject $H_0$”: We reject the claim that the patient does not have the disease. This means the test indicates the patient has the disease.
– “$H_0$ is false”: The statement “the patient does not have the disease” is false. This means the patient actually does have the disease.

3. Combine the Definitions:
Therefore, the power of this test is the probability that the test indicates the patient has the disease, given that the patient truly has the disease.

4. Evaluate the Options:
– (C) describes a Type I error (false positive).
– (D) describes a Type II error (false negative).
– (E) describes a correct decision (true negative).
– (B) correctly describes power (a true positive).
✅ Answer: (B)

More AP Statistics MCQ Questions..
Scroll to Top