AP Statistics Practice Quiz: Potential Errors When Performing Tests

Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026

Test your understanding with short quizzes. This quiz has 16 questions to check your progress.

Question 1 of 16

In the context of hypothesis testing, what is a Type I error?

A)Rejecting a true null hypothesis.B)Failing to reject a true null hypothesis.C)Rejecting a false null hypothesis.D)Failing to reject a false null hypothesis.

All Questions (16)

In the context of hypothesis testing, what is a Type I error?

A) Rejecting a true null hypothesis.

B) Failing to reject a true null hypothesis.

C) Rejecting a false null hypothesis.

D) Failing to reject a false null hypothesis.

Correct Answer: A

According to the provided content, a Type I error occurs when a true null hypothesis is rejected. This is also referred to as a false positive.

A Type II error is committed under which of the following circumstances?

A) A true null hypothesis is rejected.

B) A false null hypothesis is not rejected.

C) A false null hypothesis is correctly rejected.

D) A true null hypothesis is correctly not rejected.

Correct Answer: B

The provided content defines a Type II error as an instance where a false null hypothesis is not rejected. This is also known as a false negative.

A pharmaceutical company develops a new drug to treat a disease. The null hypothesis is that the drug has no effect. After a clinical trial, they reject the null hypothesis. If, in reality, the drug is ineffective, what type of error has been made?

A) Type I error

B) Type II error

C) A correct decision

D) Standard error

Correct Answer: A

The company rejected the null hypothesis (that the drug has no effect). However, the null hypothesis was actually true (the drug is ineffective). Rejecting a true null hypothesis is the definition of a Type I error.

An engineer tests a new airplane wing design. The null hypothesis is that the new design is no stronger than the old one. The test results lead the engineer to not reject the null hypothesis. If the new design is, in fact, significantly stronger, what is the outcome of this decision?

A) A Type I error, because a true null hypothesis was rejected.

B) A Type II error, because a false null hypothesis was not rejected.

C) A correct decision, because a true null hypothesis was not rejected.

D) A correct decision, because a false null hypothesis was rejected.

Correct Answer: B

The null hypothesis (new design is no stronger) was false, but the engineer failed to reject it. According to the provided content, failing to reject a false null hypothesis is a Type II error.

The significance level of a hypothesis test, denoted by alpha (α), represents which of the following probabilities?

A) The probability of making a Type II error.

B) The probability of correctly rejecting a false null hypothesis.

C) The probability of making a Type I error if the null hypothesis is true.

D) The probability that the null hypothesis is true.

Correct Answer: C

The provided content explicitly states that the significance level, alpha, is the probability of making a Type I error if the null hypothesis is true.

If the power of a statistical test is calculated to be 0.80, what is the probability of committing a Type II error?

A) 0.80

B) 0.20

C) 0.05

D) It cannot be determined from the information given.

Correct Answer: B

The content states that the probability of a Type II error is equal to 1 minus the power of the test. Therefore, the probability of a Type II error is 1 - 0.80 = 0.20.

A researcher is planning a study and wants to decrease the probability of making a Type II error. Which of the following strategies would be most effective?

A) Decreasing the sample size.

B) Decreasing the significance level (alpha).

C) Increasing the sample size.

D) Using a smaller effect size.

Correct Answer: C

The provided content states that the probability of a Type II error decreases as the sample size, significance level, or effect size increases. Of the options provided, only increasing the sample size would decrease the probability of a Type II error.

The term 'false positive' is another name for which of the following?

A) Type I error

B) Type II error

C) Power of the test

D) Significance level

Correct Answer: A

The provided content explicitly defines a Type I error as an instance where a true null hypothesis is rejected, which is also described as a 'false positive'.

In a legal system, the null hypothesis is that the defendant is innocent. If the court wrongly convicts an innocent person, what is the consequence in statistical terms?

A) A Type I error has been made.

B) A Type II error has been made.

C) The power of the judicial process has increased.

D) The significance level was too low.

Correct Answer: A

The null hypothesis (innocence) was true, but it was rejected (the person was convicted). Rejecting a true null hypothesis is a Type I error. The consequences of this type of error are severe in this context.

Consider a situation where the consequences of a Type I error are extremely severe, such as approving a harmful new medication. How should a researcher adjust the significance level (alpha) to account for this?

A) Set a very high alpha, such as 0.10 or 0.20.

B) Set a very low alpha, such as 0.01 or 0.001.

C) Increase the sample size but keep alpha at 0.05.

D) The significance level should not be adjusted based on consequences.

Correct Answer: B

The content states that the choice of significance level (alpha) is influenced by the consequences of a Type I error. Since alpha is the probability of a Type I error, a researcher would set a very low alpha to minimize the chance of this severe error occurring.

How does increasing the significance level (e.g., from α = 0.01 to α = 0.05) affect the probabilities of Type I and Type II errors?

A) It increases the probability of a Type I error and increases the probability of a Type II error.

B) It decreases the probability of a Type I error and increases the probability of a Type II error.

C) It increases the probability of a Type I error and decreases the probability of a Type II error.

D) It decreases the probability of a Type I error and decreases the probability of a Type II error.

Correct Answer: C

By definition, the significance level alpha is the probability of a Type I error, so increasing alpha increases the probability of a Type I error. The content also states that the probability of a Type II error decreases as the significance level increases. Therefore, there is a trade-off between the two types of errors.

The power of a test is defined as:

A) The probability of making a Type I error.

B) The probability of correctly rejecting a false null hypothesis.

C) The probability of not rejecting a true null hypothesis.

D) 1 minus the probability of a Type I error.

Correct Answer: B

The provided content directly defines the power of a test as 'the probability of correctly rejecting a false null hypothesis.' This represents the test's ability to detect a real effect.

All other factors being equal, which of the following changes would result in an increase in the power of a significance test?

A) Decreasing the sample size.

B) Decreasing the effect size.

C) Decreasing the significance level (alpha).

D) Increasing the significance level (alpha).

Correct Answer: D

Power is 1 minus the probability of a Type II error. To increase power, one must decrease the probability of a Type II error. The content states that the probability of a Type II error decreases as the significance level increases. Therefore, increasing alpha increases the power of the test.

A 'false negative' in a medical screening test for a disease corresponds to what type of error in hypothesis testing?

A) Type I error

B) Type II error

C) Standard error

D) Sampling error

Correct Answer: B

A 'false negative' means the test failed to detect a condition that was actually present. In hypothesis testing (where H₀: no disease), this means failing to reject a false null hypothesis, which is the definition of a Type II error.

A quality control manager for a factory producing light bulbs takes a sample to test if the average lifespan is less than the advertised 1000 hours (H₀: μ = 1000 vs Hₐ: μ < 1000). The manager fails to reject the null hypothesis. If the true average lifespan of all bulbs is actually 980 hours, what is the consequence of the manager's decision?

A) A Type I error occurred, and the company will mistakenly recall a good product.

B) A Type II error occurred, and the company will continue to sell a product that does not meet its advertised standard.

C) A correct decision was made, and the product is up to standard.

D) The power of the test was too high, leading to an incorrect conclusion.

Correct Answer: B

The null hypothesis (μ = 1000) was false because the true mean was 980. The manager failed to reject this false null hypothesis. This is a Type II error. The consequence is that a substandard product continues to be sold.

A researcher conducts a study with a very small sample size. What is the most likely impact of the small sample size on the probabilities of errors?

A) It increases the probability of a Type I error and decreases the probability of a Type II error.

B) It decreases the probability of a Type I error and increases the probability of a Type II error.

C) It increases the probability of both Type I and Type II errors.

D) It has no effect on the probability of either error.

Correct Answer: B

The probability of a Type I error is set by alpha and is not directly affected by sample size. However, the content states that the probability of a Type II error decreases as sample size increases. Therefore, a small sample size will lead to a higher probability of a Type II error (and consequently, lower power).