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AP Statistics Practice Quiz: Biased and Unbiased Point Estimates

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

Test your understanding with short quizzes. This quiz has 14 questions to check your progress.

Question 1 of 14

Which of the following best describes a point estimator?

All Questions (14)

Which of the following best describes a point estimator?

A) A value calculated from a population that estimates a sample statistic.

B) A value calculated from a sample that estimates a population parameter.

C) The true value of a population characteristic.

D) A measure of the variability of a population.

Correct Answer: B

Based on the provided content, "A sample statistic serves as a point estimator for the corresponding population parameter." This means a value calculated from a sample is used to estimate a value for the entire population.

An estimator is considered unbiased if which of the following is true?

A) Its value is always equal to the population parameter.

B) Its variability is zero.

C) Its average value across all possible samples is equal to the population parameter.

D) It is calculated from a very large sample.

Correct Answer: C

The provided content states, "An estimator is unbiased if its average value equals the population parameter." This refers to the average of the estimator's values over all possible samples, which is the mean of its sampling distribution.

A researcher wants to estimate the average commute time for all employees at a company. They take a random sample of 4 employees with commute times (in minutes) of 20, 30, 25, and 45. What is the point estimate for the population mean commute time?

A) 25 minutes

B) 30 minutes

C) 35 minutes

D) 45 minutes

Correct Answer: B

A sample statistic serves as a point estimator for the population parameter. To estimate the population mean, we must calculate the sample mean. The sample mean is (20 + 30 + 25 + 45) / 4 = 120 / 4 = 30 minutes.

A statistician takes many random samples of the same size from a population to estimate a parameter. They notice that the value of the sample statistic is different for each sample. Which principle does this observation illustrate?

A) An estimator is always biased.

B) An estimator exhibits variability.

C) A population parameter changes with each sample.

D) A point estimate is always equal to the parameter.

Correct Answer: B

The content states, "An estimator exhibits variability that can be modeled using probability." The fact that the sample statistic's value changes from sample to sample is the definition of this variability.

The sampling distribution of a certain statistic used to estimate a population mean has a mean that is exactly equal to the true population mean. How would this statistic be described as an estimator?

A) Biased, because it has a sampling distribution.

B) Unbiased, because its average value equals the population parameter.

C) Biased, because it exhibits variability.

D) Unbiased, because it was calculated from a random sample.

Correct Answer: B

The definition of an unbiased estimator is that its average value (the mean of its sampling distribution) is equal to the population parameter it is intended to estimate.

In statistical inference, a sample statistic is used for what primary purpose?

A) To define the size of the population.

B) To serve as a point estimator for a population parameter.

C) To prove a hypothesis with absolute certainty.

D) To eliminate all variability from the data.

Correct Answer: B

The content directly states, "A sample statistic serves as a point estimator for the corresponding population parameter."

Suppose a statistic consistently underestimates the population parameter it is intended to measure. This means that the average value of the statistic across all possible samples is less than the true parameter. This statistic is an example of:

A) An unbiased estimator.

B) A biased estimator.

C) A population parameter.

D) An estimator with no variability.

Correct Answer: B

An estimator is unbiased if its average value equals the population parameter. Since this statistic's average value is less than the parameter (it consistently underestimates), it does not equal the parameter and is therefore biased.

In a random sample of 500 light bulbs from a factory, 15 were found to be defective. What is the point estimate for the proportion of all light bulbs from this factory that are defective?

A) 15

B) 0.03

C) 0.97

D) 500

Correct Answer: B

The sample proportion serves as the point estimator for the population proportion. It is calculated by dividing the number of successes (defective bulbs) by the sample size. The estimate is 15 / 500 = 0.03.

The concept that an estimator's variability can be "modeled using probability" implies which of the following?

A) The estimator's value is completely random and unpredictable.

B) We can describe the long-run pattern of the estimator's values using a probability distribution.

C) The estimator will always be correct if the probability is high enough.

D) The variability of an estimator is a fixed, unchanging number for all situations.

Correct Answer: B

To say variability can be "modeled using probability" refers to the creation of a sampling distribution, which is a probability distribution that describes the long-run behavior and pattern of a sample statistic's values over many samples.

A sample mean is an unbiased estimator of the population mean. Does this guarantee that a single sample mean, calculated from a random sample, will be equal to the population mean?

A) Yes, because 'unbiased' means every estimate is perfectly accurate.

B) Yes, but only if the sample is perfectly random and large enough.

C) No, because an estimator exhibits variability, meaning a single estimate will likely differ from the parameter.

D) No, because the sample mean is actually a biased estimator.

Correct Answer: C

The term 'unbiased' means the average of all possible sample means will equal the population mean. However, any single estimator exhibits variability, meaning a specific sample mean will likely not be exactly equal to the population mean due to random sampling variation.

A city's planning department wants to estimate the true proportion of residents who support building a new park. They survey a sample of residents and calculate the proportion in the sample who show support. This sample proportion is a:

A) Population parameter.

B) Point estimator.

C) Source of bias.

D) Probability model.

Correct Answer: B

The content states that a sample statistic (like the sample proportion) serves as a point estimator for the corresponding population parameter (the true proportion of all residents).

To explain why a sample statistic is an unbiased estimator, one must show that:

A) The statistic has the smallest possible variability.

B) The mean of the statistic's sampling distribution is equal to the population parameter.

C) The statistic was calculated from a sample taken without replacement.

D) The value of the statistic is a positive number.

Correct Answer: B

The fundamental reason an estimator is unbiased is that its average value, which is the mean of its sampling distribution, equals the population parameter it is estimating.

A national poll reports that a point estimate for the proportion of adults who own a pet is 0.68. The true proportion of all adults in the country who own a pet is an example of a:

A) Sample statistic.

B) Point estimator.

C) Population parameter.

D) Biased estimate.

Correct Answer: C

The point estimate (0.68) is a sample statistic used to estimate the population parameter. The "true proportion of all adults" is the value for the entire population, which is the definition of a population parameter.

An engineer develops a new device to estimate the true concentration of a chemical. After many measurements of the same solution, they find that the average of their estimates is correct, but the individual estimates vary widely. Which statement best describes the device's estimates?

A) Biased and with high variability.

B) Unbiased and with high variability.

C) Biased and with low variability.

D) Unbiased and with low variability.

Correct Answer: B

The estimator is unbiased because its average value equals the population parameter (the true concentration). It has high variability because the individual estimates "vary widely." The content distinguishes between the average value (related to bias) and the spread of values (variability).