AP STATISTICS –QUESTIONS AND CORRECT ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A |
INSTANT DOWNLOAD PDF.
*Core Domains*
*- Exploring Data*
*- Sampling and Experimentation*
*- Probability and Simulation*
*- Random Variables*
*- Sampling Distributions*
*- Inference for Proportions*
*- Inference for Means*
*- Chi-Square Procedures*
*- Inference for Regression*
*Introduction*
*This assessment is designed to measure proficiency in fundamental statistical concepts and their practica
Section One: Questions 1–100
1. A researcher wants to determine if a new fertilizer increases crop yield. What is the primary purpose of using a
control group in this experiment?
A. To ensure the sample size is large enough.
B. To provide a baseline for comparison to isolate the effect of the fertilizer.
,🟢 C. To minimize the influence of lurking variables and account for the placebo effect.
D. To guarantee that all plants grow at the same rate.
🔴 RATIONALE: A control group allows researchers to observe the effects of the experimental treatment compared to
a group that did not receive it, thereby isolating the variable being tested.
2. In a normal distribution with a mean of 50 and a standard deviation of 10, what percentage of observations fall
between 30 and 70?
A. 68%
B. 95%
🟢 C. 99.7%
D. 50%
🔴 RATIONALE: According to the Empirical Rule, approximately 99.7% of data in a normal distribution falls within
three standard deviations of the mean, and 30 and 70 are three standard deviations away.
3. Which of the following is an example of a voluntary response sample?
A. Randomly selecting phone numbers from a directory.
B. Surveying every tenth person who enters a shopping mall.
🟢 C. A radio station asking listeners to call in to share their opinion on a new law.
D. Interviewing students chosen from an alphabetical list of the school roster.
🔴 RATIONALE: Voluntary response samples occur when subjects choose to participate themselves, which often
leads to biased results as those with strong opinions are more likely to respond.
4. If two events, A and B, are mutually exclusive, what is P(A and B)?
A. P(A) * P(B)
🟢 B. 0
,C. P(A) + P(B)
D. 1
🔴 RATIONALE: Mutually exclusive events cannot occur at the same time; therefore, the probability of both occurring
simultaneously is zero.
5. A study finds a correlation of 0.85 between hours studied and test scores. What does this indicate?
🟢 A. A strong positive linear relationship between study hours and test scores.
B. That studying causes higher test scores.
C. That the variables have no relationship.
D. That 85% of test scores are determined by study time.
🔴 RATIONALE: A correlation coefficient of 0.85 indicates a strong positive linear association, but it does not imply
causation.
6. Which measure of center is most resistant to outliers?
A. Mean
🟢 B. Median
C. Mode
D. Range
🔴 RATIONALE: The median is based on the position of the middle value, making it unaffected by the extreme values
that can significantly pull the mean.
7. A sample proportion is used to estimate a population proportion. As the sample size increases, what happens to
the standard deviation of the sampling distribution?
🟢 A. It decreases.
B. It increases.
, C. It remains constant.
D. It becomes equal to the population mean.
🔴 RATIONALE: The standard deviation of the sampling distribution of a proportion is inversely proportional to the
square root of the sample size, so increasing the sample size decreases the standard deviation.
8. A Type I error in hypothesis testing occurs when:
A. The null hypothesis is false and we fail to reject it.
🟢 B. The null hypothesis is true and we reject it.
C. The alternative hypothesis is true and we reject it.
D. The sample size is too small to draw a conclusion.
🔴 RATIONALE: A Type I error, often called a false positive, occurs when a researcher incorrectly rejects a true null
hypothesis.
9. When constructing a 95% confidence interval for a population mean, what is the impact of increasing the
confidence level to 99%?
🟢 A. The interval becomes wider.
B. The interval becomes narrower.
C. The interval remains the same size.
D. The sample mean changes.
🔴 RATIONALE: To be more confident, the interval must encompass a larger area of the distribution, which requires a
wider margin of error.
10. A residual plot for a linear regression model shows a clear curved pattern. What does this suggest?
A. The linear model is a good fit.
B. The correlation is 1.0.
INSTANT DOWNLOAD PDF.
*Core Domains*
*- Exploring Data*
*- Sampling and Experimentation*
*- Probability and Simulation*
*- Random Variables*
*- Sampling Distributions*
*- Inference for Proportions*
*- Inference for Means*
*- Chi-Square Procedures*
*- Inference for Regression*
*Introduction*
*This assessment is designed to measure proficiency in fundamental statistical concepts and their practica
Section One: Questions 1–100
1. A researcher wants to determine if a new fertilizer increases crop yield. What is the primary purpose of using a
control group in this experiment?
A. To ensure the sample size is large enough.
B. To provide a baseline for comparison to isolate the effect of the fertilizer.
,🟢 C. To minimize the influence of lurking variables and account for the placebo effect.
D. To guarantee that all plants grow at the same rate.
🔴 RATIONALE: A control group allows researchers to observe the effects of the experimental treatment compared to
a group that did not receive it, thereby isolating the variable being tested.
2. In a normal distribution with a mean of 50 and a standard deviation of 10, what percentage of observations fall
between 30 and 70?
A. 68%
B. 95%
🟢 C. 99.7%
D. 50%
🔴 RATIONALE: According to the Empirical Rule, approximately 99.7% of data in a normal distribution falls within
three standard deviations of the mean, and 30 and 70 are three standard deviations away.
3. Which of the following is an example of a voluntary response sample?
A. Randomly selecting phone numbers from a directory.
B. Surveying every tenth person who enters a shopping mall.
🟢 C. A radio station asking listeners to call in to share their opinion on a new law.
D. Interviewing students chosen from an alphabetical list of the school roster.
🔴 RATIONALE: Voluntary response samples occur when subjects choose to participate themselves, which often
leads to biased results as those with strong opinions are more likely to respond.
4. If two events, A and B, are mutually exclusive, what is P(A and B)?
A. P(A) * P(B)
🟢 B. 0
,C. P(A) + P(B)
D. 1
🔴 RATIONALE: Mutually exclusive events cannot occur at the same time; therefore, the probability of both occurring
simultaneously is zero.
5. A study finds a correlation of 0.85 between hours studied and test scores. What does this indicate?
🟢 A. A strong positive linear relationship between study hours and test scores.
B. That studying causes higher test scores.
C. That the variables have no relationship.
D. That 85% of test scores are determined by study time.
🔴 RATIONALE: A correlation coefficient of 0.85 indicates a strong positive linear association, but it does not imply
causation.
6. Which measure of center is most resistant to outliers?
A. Mean
🟢 B. Median
C. Mode
D. Range
🔴 RATIONALE: The median is based on the position of the middle value, making it unaffected by the extreme values
that can significantly pull the mean.
7. A sample proportion is used to estimate a population proportion. As the sample size increases, what happens to
the standard deviation of the sampling distribution?
🟢 A. It decreases.
B. It increases.
, C. It remains constant.
D. It becomes equal to the population mean.
🔴 RATIONALE: The standard deviation of the sampling distribution of a proportion is inversely proportional to the
square root of the sample size, so increasing the sample size decreases the standard deviation.
8. A Type I error in hypothesis testing occurs when:
A. The null hypothesis is false and we fail to reject it.
🟢 B. The null hypothesis is true and we reject it.
C. The alternative hypothesis is true and we reject it.
D. The sample size is too small to draw a conclusion.
🔴 RATIONALE: A Type I error, often called a false positive, occurs when a researcher incorrectly rejects a true null
hypothesis.
9. When constructing a 95% confidence interval for a population mean, what is the impact of increasing the
confidence level to 99%?
🟢 A. The interval becomes wider.
B. The interval becomes narrower.
C. The interval remains the same size.
D. The sample mean changes.
🔴 RATIONALE: To be more confident, the interval must encompass a larger area of the distribution, which requires a
wider margin of error.
10. A residual plot for a linear regression model shows a clear curved pattern. What does this suggest?
A. The linear model is a good fit.
B. The correlation is 1.0.
