AP STATISTICS – QUESTIONS AND CORRECT ANSWERS (VERIFIED ANSWERS) PLUS RATIONALES 2026 Q&A
| INSTANT DOWNLOAD PDF.
*Core Domains*
Data Collection and Experimental Design
Exploratory Data Analysis
Probability and Random Variables
Sampling Distributions
Inference for Proportions
Inference for Means
Chi-Square Procedures
Linear Regression and Correlation
Statistical Ethics and Professional Standards
*Introduction*
This comprehensive assessment is designed to evaluate a student's proficiency in the core concepts of advanced
statistics. The purpose of this exam is to measure mastery of data interpretation, statistical inference, and the rigorous
application of probability models to real-world scenarios. Students will be assessed on their ability to analyze data,
,select appropriate tests, and demonstrate sound decision-making through professional statistical methodology. The
examination utilizes a multiple-choice structure, incorporating complex, scenario-based problems that emphasize
critical thinking. Success on this exam requires an integrated understanding of theoretical foundations, regulatory
compliance in research, and the nuanced interpretation of quantitative results.
SECTION ONE: QUESTIONS 1–100
1. A researcher wants to determine if a new fertilizer increases crop yield. She randomly assigns plots of land to
receive either the new fertilizer or a standard fertilizer. What type of study is this?
A. Observational study
B. Simple random sample
🟢 C. Randomized experiment
D. Stratified sample
🔴 RATIONALE: The study involves the active manipulation of an independent variable (the type of fertilizer) and
random assignment of subjects (plots), which defines a randomized experiment.
2. A local news station asks viewers to call in and vote on a controversial issue. What is the primary concern with
this sampling method?
A. It is too expensive
🟢 B. It suffers from voluntary response bias
C. It lacks a control group
D. It has a high margin of error
🔴 RATIONALE: Voluntary response samples only include individuals who choose to participate, often leading to
strong bias toward those with extreme opinions.
3. Which of the following describes the standard deviation of a sampling distribution of the sample mean?
,A. The population standard deviation
🟢 B. The standard error of the mean
C. The margin of error
D. The variance
🔴 RATIONALE: The standard deviation of the sampling distribution of the sample mean (σxˉ ) is referred to as the
standard error of the mean, calculated as σ/ n .
4. In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
A. 68%
B. 95%
C. 99.7%
🟢 D. 95.4%
🔴 RATIONALE: According to the empirical rule, approximately 95% (specifically 95.4%) of data in a normal
distribution lies within two standard deviations of the mean.
5. A study finds a correlation of r = −0.85 between two variables. What does this indicate?
A. A weak positive linear relationship
B. A weak negative linear relationship
🟢 C. A strong negative linear relationship
D. No relationship
🔴 RATIONALE: The correlation coefficient r ranges from -1 to 1. A value of -0.85 indicates a strong linear relationship
with a negative slope.
6. Which condition must be met to perform a Z-test for a population proportion?
A. The sample size must be at least 100
B. The population must be normally distributed
🟢 C. The sample must show at least 10 successes and 10 failures
D. The data must be quantitative
, 🔴 RATIONALE: For proportions, the Large Counts Condition requires np ≥ 10 and n(1 − p) ≥ 10 to ensure the
sampling distribution of the proportion is approximately normal.
7. What is the probability of a Type I error?
A. The power of the test
B. The p-value
🟢 C. The significance level (α)
D. The probability of a Type II error (β )
🔴 RATIONALE: A Type I error occurs when the null hypothesis is rejected when it is actually true. The probability of
this is defined by the chosen significance level, α.
8. A data set has an outlier that is much larger than the rest of the data. Which measure of center is most resistant
to this outlier?
A. Mean
🟢 B. Median
C. Range
D. Standard deviation
🔴 RATIONALE: The median is based on the ordering of values and is resistant to extreme values, whereas the mean
is sensitive to every value in the set.
9. In a hypothesis test, if the p-value is 0.03 and the significance level is 0.05, what is the correct decision?
🟢 A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis
D. Conduct a new study
🔴 RATIONALE: When the p-value is less than or equal to the significance level (α), we reject the null hypothesis
because the results are statistically significant.
| INSTANT DOWNLOAD PDF.
*Core Domains*
Data Collection and Experimental Design
Exploratory Data Analysis
Probability and Random Variables
Sampling Distributions
Inference for Proportions
Inference for Means
Chi-Square Procedures
Linear Regression and Correlation
Statistical Ethics and Professional Standards
*Introduction*
This comprehensive assessment is designed to evaluate a student's proficiency in the core concepts of advanced
statistics. The purpose of this exam is to measure mastery of data interpretation, statistical inference, and the rigorous
application of probability models to real-world scenarios. Students will be assessed on their ability to analyze data,
,select appropriate tests, and demonstrate sound decision-making through professional statistical methodology. The
examination utilizes a multiple-choice structure, incorporating complex, scenario-based problems that emphasize
critical thinking. Success on this exam requires an integrated understanding of theoretical foundations, regulatory
compliance in research, and the nuanced interpretation of quantitative results.
SECTION ONE: QUESTIONS 1–100
1. A researcher wants to determine if a new fertilizer increases crop yield. She randomly assigns plots of land to
receive either the new fertilizer or a standard fertilizer. What type of study is this?
A. Observational study
B. Simple random sample
🟢 C. Randomized experiment
D. Stratified sample
🔴 RATIONALE: The study involves the active manipulation of an independent variable (the type of fertilizer) and
random assignment of subjects (plots), which defines a randomized experiment.
2. A local news station asks viewers to call in and vote on a controversial issue. What is the primary concern with
this sampling method?
A. It is too expensive
🟢 B. It suffers from voluntary response bias
C. It lacks a control group
D. It has a high margin of error
🔴 RATIONALE: Voluntary response samples only include individuals who choose to participate, often leading to
strong bias toward those with extreme opinions.
3. Which of the following describes the standard deviation of a sampling distribution of the sample mean?
,A. The population standard deviation
🟢 B. The standard error of the mean
C. The margin of error
D. The variance
🔴 RATIONALE: The standard deviation of the sampling distribution of the sample mean (σxˉ ) is referred to as the
standard error of the mean, calculated as σ/ n .
4. In a normal distribution, approximately what percentage of data falls within two standard deviations of the mean?
A. 68%
B. 95%
C. 99.7%
🟢 D. 95.4%
🔴 RATIONALE: According to the empirical rule, approximately 95% (specifically 95.4%) of data in a normal
distribution lies within two standard deviations of the mean.
5. A study finds a correlation of r = −0.85 between two variables. What does this indicate?
A. A weak positive linear relationship
B. A weak negative linear relationship
🟢 C. A strong negative linear relationship
D. No relationship
🔴 RATIONALE: The correlation coefficient r ranges from -1 to 1. A value of -0.85 indicates a strong linear relationship
with a negative slope.
6. Which condition must be met to perform a Z-test for a population proportion?
A. The sample size must be at least 100
B. The population must be normally distributed
🟢 C. The sample must show at least 10 successes and 10 failures
D. The data must be quantitative
, 🔴 RATIONALE: For proportions, the Large Counts Condition requires np ≥ 10 and n(1 − p) ≥ 10 to ensure the
sampling distribution of the proportion is approximately normal.
7. What is the probability of a Type I error?
A. The power of the test
B. The p-value
🟢 C. The significance level (α)
D. The probability of a Type II error (β )
🔴 RATIONALE: A Type I error occurs when the null hypothesis is rejected when it is actually true. The probability of
this is defined by the chosen significance level, α.
8. A data set has an outlier that is much larger than the rest of the data. Which measure of center is most resistant
to this outlier?
A. Mean
🟢 B. Median
C. Range
D. Standard deviation
🔴 RATIONALE: The median is based on the ordering of values and is resistant to extreme values, whereas the mean
is sensitive to every value in the set.
9. In a hypothesis test, if the p-value is 0.03 and the significance level is 0.05, what is the correct decision?
🟢 A. Reject the null hypothesis
B. Fail to reject the null hypothesis
C. Accept the null hypothesis
D. Conduct a new study
🔴 RATIONALE: When the p-value is less than or equal to the significance level (α), we reject the null hypothesis
because the results are statistically significant.
