AP STATISTICS EXAM TESTBANK| 300 REVISED QUESTIONS
AND ANSWERS 2026/2027 | VERIFIED ANSWERS PLUS
RATIONALES | GRADED Q&A COMPREHENSIVE STUDY GUIDE
VERIFIED LATEST 2027
1. A discrete random variable $X$ has a probability distribution where the sum of all
possible probabilities must equal which of the following values?
A. 0
B. 0.5
C. 1
D. Infinity
Answer: C
A fundamental axiom of probability is that the sum of the probabilities of all possible disjoint
outcomes in a sample space must equal 1.
2. A researcher measures the height and weight of adult dogs. Which numerical summary
is most appropriate to describe the center and spread of dog weight if the distribution is
strongly right-skewed with extreme outliers?
A. Mean and standard deviation
B. Median and interquartile range
C. Mean and range
D. Mode and variance
Answer: B
For skewed distributions or distributions with extreme outliers, the median and interquartile
range (IQR) are resistant measures of center and spread, whereas the mean and standard
deviation are heavily influenced by outliers.
3. In a regression analysis relating advertising expenditure (in thousands of dollars) to
monthly sales revenue (in thousands of dollars), the least-squares regression line is given by
$\hat{y} = 12.5 + 4.2x$. What is the correct interpretation of the slope coefficient?
A. For every thousand-dollar increase in advertising expenditure, the predicted monthly sales
revenue increases by $4.2.
B. For every thousand-dollar increase in advertising expenditure, the predicted monthly sales
revenue increases by $4,200.
C. When advertising expenditure is zero, predicted monthly sales revenue is $4,200.
D. Predicted monthly sales revenue increases by $12,500 for every unit increase in advertising.
,Answer: B
The slope represents the expected change in the response variable ($y$) for a one-unit
increase in the explanatory variable ($x$). Because both variables are measured in thousands
of dollars, an increase of 1 unit ($1,000) in $x$ leads to an increase of $4.2$ thousand dollars,
which equals $4,200 in sales revenue.
4. A standardized reading test has a mean score of 100 and a standard deviation of 15.
Assuming the scores are normally distributed, what proportion of students score above
130?
A. 0.0228
B. 0.0500
C. 0.1587
D. 0.9772
Answer: A
First, calculate the z-score for 130: $z = (130 - 100) / 15 = 2.0$. Using the standard normal
distribution table or calculator, the area to the left of $z = 2.0$ is 0.9772. Therefore, the
proportion scoring above 130 is $1 - 0.9772 = 0.0228$.
5. An agricultural researcher tests four different fertilizer treatments on corn yield. Twenty
plots of land are randomly assigned to the four treatments (5 plots per treatment). This
study is best described as which of the following?
A. An observational study with blocking
B. A completely randomized design experiment
C. A matched-pairs experiment
D. A randomized block design experiment
Answer: B
In a completely randomized design, experimental units (the 20 plots) are assigned completely
at random to all treatments, ensuring that all treatments have an equal chance of being
assigned to any plot and helping control for confounding variables.
6. Which of the following statements about the correlation coefficient ($r$) is true?
A. A correlation of $0.85$ indicates a stronger linear relationship than a correlation of $-0.90$.
B. The value of $r$ changes when the units of measurement for $x$ and $y$ are changed.
C. The square of the correlation coefficient ($r^2$) represents the proportion of variability in
$y$ that is explained by the linear relationship with $x$.
D. Correlation implies causation if the sample size is greater than 30.
Answer: C
,The coefficient of determination, $r^2$, measures the proportion of total variation in the
response variable that is accounted for by the linear regression model. Correlation does not
imply causation, and the strength of correlation depends on magnitude, making $-0.90$
stronger than $0.85$.
7. A bag contains 4 red marbles, 3 blue marbles, and 3 green marbles. Two marbles are
drawn at random without replacement. What is the probability that both marbles are red?
A. $4/25$
B. $2/15$
C. $6/25$
D. $4/9$
Answer: B
The total number of marbles is 10. The probability of drawing a red first is $4/10$. Without
replacement, 3 red marbles remain out of 9 total marbles, so the probability of drawing a red
second is $3/9$. The combined probability is $(4/10) \times (3/9) = 12/90 = 2/15$.
8. In a hypothesis test for a single population mean, the calculated p-value is 0.034 and the
significance level ($\alpha$) is set at 0.05. What is the appropriate conclusion?
A. Reject the null hypothesis; there is sufficient evidence that the alternative hypothesis is true.
B. Fail to reject the null hypothesis; there is insufficient evidence that the alternative hypothesis
is true.
C. Accept the null hypothesis because the p-value is less than 0.05.
D. Fail to reject the alternative hypothesis because the p-value is greater than 0.01.
Answer: A
Since the p-value ($0.034$) is less than the significance level ($\alpha = 0.05$), we reject the
null hypothesis and conclude that there is statistically significant evidence in favor of the
alternative hypothesis.
9. A candy manufacturer claims that 20% of its chocolate candies are blue. A quality
control inspector takes a random sample of 150 candies and finds that 36 are blue. Which
hypothesis test should the inspector use to test the manufacturer's claim?
A. Two-sample z-test for proportions
B. One-sample t-test for a mean
C. One-sample z-test for a proportion
D. Chi-square goodness-of-fit test
Answer: C
, The inspector is testing a claim about a single population proportion ($p = 0.20$) based on a
single categorical sample, which requires a one-sample z-test for a proportion.
10. Which of the following graphical displays is most appropriate for showing the
relationship between two quantitative variables?
A. Boxplot
B. Bar chart
C. Scatterplot
D. Pie chart
Answer: C
A scatterplot is specifically designed to display bivariate quantitative data, allowing analysts
to visualize patterns, trends, associations, and outliers between two numerical variables.
11. A study finds a strong positive correlation between ice cream sales and rates of sunburn
in a coastal town. What is the best explanation for this relationship?
A. Eating ice cream causes sunburn.
B. Getting a sunburn causes people to buy ice cream.
C. A lurking variable, such as temperature or sunny weather, drives both variables.
D. The correlation is purely coincidental and has no logical basis.
Answer: C
Correlation does not imply causation. In this scenario, temperature (or sunny weather) acts as
a lurking variable that causes both increased ice cream consumption and higher rates of
sunburn.
12. The distribution of household incomes in a large metropolitan area is heavily right-
skewed. If a random sample of 100 households is selected, what can be said about the
sampling distribution of the sample mean income?
A. It will be heavily right-skewed.
B. It will be approximately normal due to the Central Limit Theorem.
C. It will be uniformly distributed.
D. It will have the exact same shape as the population distribution.
Answer: B
According to the Central Limit Theorem, when the sample size is sufficiently large ($n \ge
30$), the sampling distribution of the sample mean will be approximately normal, regardless
of the shape of the underlying population distribution.
13. In a criminal trial, a Type I error corresponds to which of the following scenarios?
AND ANSWERS 2026/2027 | VERIFIED ANSWERS PLUS
RATIONALES | GRADED Q&A COMPREHENSIVE STUDY GUIDE
VERIFIED LATEST 2027
1. A discrete random variable $X$ has a probability distribution where the sum of all
possible probabilities must equal which of the following values?
A. 0
B. 0.5
C. 1
D. Infinity
Answer: C
A fundamental axiom of probability is that the sum of the probabilities of all possible disjoint
outcomes in a sample space must equal 1.
2. A researcher measures the height and weight of adult dogs. Which numerical summary
is most appropriate to describe the center and spread of dog weight if the distribution is
strongly right-skewed with extreme outliers?
A. Mean and standard deviation
B. Median and interquartile range
C. Mean and range
D. Mode and variance
Answer: B
For skewed distributions or distributions with extreme outliers, the median and interquartile
range (IQR) are resistant measures of center and spread, whereas the mean and standard
deviation are heavily influenced by outliers.
3. In a regression analysis relating advertising expenditure (in thousands of dollars) to
monthly sales revenue (in thousands of dollars), the least-squares regression line is given by
$\hat{y} = 12.5 + 4.2x$. What is the correct interpretation of the slope coefficient?
A. For every thousand-dollar increase in advertising expenditure, the predicted monthly sales
revenue increases by $4.2.
B. For every thousand-dollar increase in advertising expenditure, the predicted monthly sales
revenue increases by $4,200.
C. When advertising expenditure is zero, predicted monthly sales revenue is $4,200.
D. Predicted monthly sales revenue increases by $12,500 for every unit increase in advertising.
,Answer: B
The slope represents the expected change in the response variable ($y$) for a one-unit
increase in the explanatory variable ($x$). Because both variables are measured in thousands
of dollars, an increase of 1 unit ($1,000) in $x$ leads to an increase of $4.2$ thousand dollars,
which equals $4,200 in sales revenue.
4. A standardized reading test has a mean score of 100 and a standard deviation of 15.
Assuming the scores are normally distributed, what proportion of students score above
130?
A. 0.0228
B. 0.0500
C. 0.1587
D. 0.9772
Answer: A
First, calculate the z-score for 130: $z = (130 - 100) / 15 = 2.0$. Using the standard normal
distribution table or calculator, the area to the left of $z = 2.0$ is 0.9772. Therefore, the
proportion scoring above 130 is $1 - 0.9772 = 0.0228$.
5. An agricultural researcher tests four different fertilizer treatments on corn yield. Twenty
plots of land are randomly assigned to the four treatments (5 plots per treatment). This
study is best described as which of the following?
A. An observational study with blocking
B. A completely randomized design experiment
C. A matched-pairs experiment
D. A randomized block design experiment
Answer: B
In a completely randomized design, experimental units (the 20 plots) are assigned completely
at random to all treatments, ensuring that all treatments have an equal chance of being
assigned to any plot and helping control for confounding variables.
6. Which of the following statements about the correlation coefficient ($r$) is true?
A. A correlation of $0.85$ indicates a stronger linear relationship than a correlation of $-0.90$.
B. The value of $r$ changes when the units of measurement for $x$ and $y$ are changed.
C. The square of the correlation coefficient ($r^2$) represents the proportion of variability in
$y$ that is explained by the linear relationship with $x$.
D. Correlation implies causation if the sample size is greater than 30.
Answer: C
,The coefficient of determination, $r^2$, measures the proportion of total variation in the
response variable that is accounted for by the linear regression model. Correlation does not
imply causation, and the strength of correlation depends on magnitude, making $-0.90$
stronger than $0.85$.
7. A bag contains 4 red marbles, 3 blue marbles, and 3 green marbles. Two marbles are
drawn at random without replacement. What is the probability that both marbles are red?
A. $4/25$
B. $2/15$
C. $6/25$
D. $4/9$
Answer: B
The total number of marbles is 10. The probability of drawing a red first is $4/10$. Without
replacement, 3 red marbles remain out of 9 total marbles, so the probability of drawing a red
second is $3/9$. The combined probability is $(4/10) \times (3/9) = 12/90 = 2/15$.
8. In a hypothesis test for a single population mean, the calculated p-value is 0.034 and the
significance level ($\alpha$) is set at 0.05. What is the appropriate conclusion?
A. Reject the null hypothesis; there is sufficient evidence that the alternative hypothesis is true.
B. Fail to reject the null hypothesis; there is insufficient evidence that the alternative hypothesis
is true.
C. Accept the null hypothesis because the p-value is less than 0.05.
D. Fail to reject the alternative hypothesis because the p-value is greater than 0.01.
Answer: A
Since the p-value ($0.034$) is less than the significance level ($\alpha = 0.05$), we reject the
null hypothesis and conclude that there is statistically significant evidence in favor of the
alternative hypothesis.
9. A candy manufacturer claims that 20% of its chocolate candies are blue. A quality
control inspector takes a random sample of 150 candies and finds that 36 are blue. Which
hypothesis test should the inspector use to test the manufacturer's claim?
A. Two-sample z-test for proportions
B. One-sample t-test for a mean
C. One-sample z-test for a proportion
D. Chi-square goodness-of-fit test
Answer: C
, The inspector is testing a claim about a single population proportion ($p = 0.20$) based on a
single categorical sample, which requires a one-sample z-test for a proportion.
10. Which of the following graphical displays is most appropriate for showing the
relationship between two quantitative variables?
A. Boxplot
B. Bar chart
C. Scatterplot
D. Pie chart
Answer: C
A scatterplot is specifically designed to display bivariate quantitative data, allowing analysts
to visualize patterns, trends, associations, and outliers between two numerical variables.
11. A study finds a strong positive correlation between ice cream sales and rates of sunburn
in a coastal town. What is the best explanation for this relationship?
A. Eating ice cream causes sunburn.
B. Getting a sunburn causes people to buy ice cream.
C. A lurking variable, such as temperature or sunny weather, drives both variables.
D. The correlation is purely coincidental and has no logical basis.
Answer: C
Correlation does not imply causation. In this scenario, temperature (or sunny weather) acts as
a lurking variable that causes both increased ice cream consumption and higher rates of
sunburn.
12. The distribution of household incomes in a large metropolitan area is heavily right-
skewed. If a random sample of 100 households is selected, what can be said about the
sampling distribution of the sample mean income?
A. It will be heavily right-skewed.
B. It will be approximately normal due to the Central Limit Theorem.
C. It will be uniformly distributed.
D. It will have the exact same shape as the population distribution.
Answer: B
According to the Central Limit Theorem, when the sample size is sufficiently large ($n \ge
30$), the sampling distribution of the sample mean will be approximately normal, regardless
of the shape of the underlying population distribution.
13. In a criminal trial, a Type I error corresponds to which of the following scenarios?
