Free AP Statistics Practice Exam (PDF)

This free AP Statistics practice exam hits the topics students lose the most points on: interpreting confidence intervals and p-values correctly, checking conditions before inference, conditional probability, and expected value. The free-response section includes a complete one-proportion z-test worked through all four rubric components — hypotheses, conditions, mechanics, and a conclusion in context. View it online or download the print-ready PDF; no account needed.

1. Question 12 marks · Shape, center & spread
   A distribution of household incomes is strongly skewed to the right. Which of the following is most likely true?
   • A.
     The mean is greater than the median
   • B.
     The mean is less than the median
   • C.
     The mean equals the median
   • D.
     The median is pulled toward the high incomes
   • E.
     The standard deviation is zero
2. Question 22 marks · Resistant statistics
   A data set of 25 house prices has one extreme outlier added to it. Which pair of statistics is MOST resistant to the outlier?
   • A.
     Mean and standard deviation
   • B.
     Mean and range
   • C.
     Median and IQR
   • D.
     Median and standard deviation
   • E.
     Range and IQR
3. Question 32 marks · z-scores
   Scores on a test are approximately normal with mean 70 and standard deviation 10. A student scores 85. The z-score is:
   • A.
     $1.5$, meaning the score is 1.5 standard deviations above the mean
   • B.
     $1.5$, meaning the score is 1.5 points above the mean
   • C.
     $15$, the distance from the mean
   • D.
     $0.85$, the percentile of the score
   • E.
     $-1.5$, since most students scored lower
4. Question 42 marks · Regression & r-squared
   A least-squares regression of exam score on hours studied has correlation $r = 0.8$. Which statement is correct?
   • A.
     80 percent of the variation in scores is explained by the regression
   • B.
     64 percent of the variation in scores is explained by the linear relationship with hours studied
   • C.
     Each extra hour of study causes a 0.8-point score increase
   • D.
     The regression predicts scores correctly 80 percent of the time
   • E.
     The residuals have correlation 0.8 with the predictor
5. Question 52 marks · Sampling methods
   A principal wants a sample of 100 students that reflects the proportions of freshmen, sophomores, juniors, and seniors in the school. She randomly selects students separately from each grade, in proportion to grade size. This design is:
   • A.
     A simple random sample
   • B.
     A stratified random sample
   • C.
     A cluster sample
   • D.
     A systematic sample
   • E.
     A convenience sample
6. Question 62 marks · Experimental design
   In a comparative experiment, the primary purpose of RANDOM ASSIGNMENT to treatments is to:
   • A.
     guarantee the sample represents the population
   • B.
     eliminate all variability between subjects
   • C.
     balance the effects of lurking variables across treatment groups
   • D.
     ensure the placebo effect does not occur
   • E.
     increase the sample size
7. Question 72 marks · Conditional probability
   At a school of 200 students, 120 are juniors and 80 are seniors. Forty-eight juniors and 40 seniors have part-time jobs. If a randomly selected student is a senior, the probability that they have a part-time job is:
   • A.
     $0.20$
   • B.
     $0.44$
   • C.
     $0.50$
   • D.
     $0.45$
   • E.
     $0.40$
8. Question 82 marks · Independence
   Events $A$ and $B$ have $P(A) = 0.4$, $P(B) = 0.5$, and $P(A \cap B) = 0.2$. Which is true?
   • A.
     $A$ and $B$ are mutually exclusive
   • B.
     A$ and $B$ are independent, since $P(A)P(B) = P(A \cap B)

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   • C.
     A$ and $B$ are dependent, since $P(A \cap B) \neq 0

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   • D.
     $P(A \cup B) = 0.9$
   • E.
     $A$ and $B$ cannot both occur
9. Question 92 marks · Binomial setting
   Which of the following scenarios describes a binomial random variable?
   • A.
     Counting made baskets in 20 independent free throws, each with success probability 0.7
   • B.
     Counting draws from a deck WITHOUT replacement until the first ace appears
   • C.
     Recording the time until a light bulb fails
   • D.
     Counting cars passing an intersection in an hour
   • E.
     Measuring the average height of 30 random students
10. Question 102 marks · Expected value
    A raffle sells 500 tickets at 2 dollars each, with a single prize worth 400 dollars. The expected net gain from buying one ticket is:
    • A.
      a loss of 1.20 dollars
    • B.
      a gain of 0.80 dollars
    • C.
      a loss of 2.00 dollars
    • D.
      a loss of 0.80 dollars
    • E.
      exactly zero
11. Question 112 marks · Sampling distributions
    A population has standard deviation $\sigma$. If the sample size is increased from $n = 25$ to $n = 100$, the standard deviation of the sampling distribution of the sample mean:
    • A.
      is divided by 4
    • B.
      is divided by 2
    • C.
      is unchanged
    • D.
      is multiplied by 2
    • E.
      becomes zero
12. Question 122 marks · Confidence interval interpretation
    A 95 percent confidence interval for a population mean is computed as $(12.1,\ 15.3)$. Which interpretation is correct?
    • A.
      There is a 95 percent probability that the population mean is between 12.1 and 15.3
    • B.
      95 percent of the data values lie between 12.1 and 15.3
    • C.
      If we repeated the sampling many times, about 95 percent of the intervals built this way would capture the population mean
    • D.
      95 percent of sample means will fall between 12.1 and 15.3
    • E.
      The sample mean has a 95 percent chance of being in the interval
13. Question 138 marks · One-proportion z-test
    Significance test. A city official claims that 60 percent of voters support a new transit measure. A polling firm takes a random sample of 600 voters from the city's 90,000 registered voters and finds 390 who support the measure. Does the sample provide convincing evidence, at the 5 percent significance level, that MORE than 60 percent of all the city's voters support the measure?
    (a)

    Define the parameter of interest and state the hypotheses.

    [2]
    (b)

    Verify that the conditions for a one-proportion z-test are met.

    [2]
    (c)

    Compute the test statistic and the p-value.

    [2]
    (d)

    State a conclusion in the context of the problem.

    [2]
14. Question 148 marks · Discrete random variables
    Expected value. An insurance company sells a one-year policy for 150 dollars. Based on historical data, in a given year a policyholder files no claim with probability 0.95, a minor claim paying out 1,000 dollars with probability 0.04, and a major claim paying out 10,000 dollars with probability 0.01.
    (a)

    Let $X$ be the payout on a randomly selected policy. Construct the probability distribution of $X$ and verify it is valid.

    [2]
    (b)

    Compute the expected payout $E(X)$ and interpret it in context.

    [2]
    (c)

    Compute the standard deviation of $X$.

    [2]
    (d)

    What is the company's expected profit per policy, and why can the company rely on this number even though individual policies vary so much?

    [2]