This ap statistics proportions quiz asks 10 multiple-choice questions on inference for proportions, and each answer comes with a short explanation.
Choose the best answer for each of the ten questions on inference for proportions. Several questions use a figure. Check each answer against the explanation to learn why the other options are tempting but wrong.
AP StatisticsCommon Core: AP Statistics Unit 3 (2026-27)
🎯 Inference for Proportions – AP Statistics math quiz
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Question 1
A random sample of 300 students is taken from a school of 1,500 students to estimate a proportion. Which condition for inference is violated?
AThe Random condition, since the school is small
BThe 10% condition, since 300 is more than 10% of 1,500
CThe Large Counts condition, since 300 is too large
DNo condition is violated, since 300 is at least 30
Question 2
In a random sample of 200 adults, 124 own a pair of running shoes. What is the standard error of the sample proportion?
A0.056
B0.0012
C0.034
D0.485
Question 3
Which critical value z* is used for a 98% confidence interval for a proportion?
A2.054
B1.960
C2.576
D2.326
Question 4
The figure shows a 95% confidence interval for the proportion of students in a district who prefer a later school start. Which statement is a correct interpretation?95% interval from a random sample of students.
AThere is a 95% probability that a randomly chosen student prefers a later start
BWe are 95% confident that the true proportion of students who prefer a later start is between 0.553 and 0.687
C95% of students in the district have a preference between 0.553 and 0.687
DThe true proportion is 0.620 with a margin of error of 95%
Question 5
A pollster plans to quadruple the sample size while keeping the same confidence level and the same expected sample proportion. What happens to the margin of error?
AIt is cut to one-fourth
BIt is doubled
CIt stays the same
DIt is cut in half
Question 6
What is the smallest sample size that gives a 95% confidence interval for a proportion with a margin of error of at most 0.04, if no prior estimate is available?
A600
B2,401
C601
D1,068
Question 7
A right-tailed z test gives z = 1.50, shown below. At the 0.05 significance level, what is the correct decision?Shaded: the P-value for a right-tailed test with z = 1.50.
AFail to reject H0, since the P-value 0.067 is greater than 0.05
BReject H0, since z = 1.50 is greater than 1
CReject H0, since the P-value 0.067 is less than 0.10
DAccept H0, since the P-value shows H0 is true
Question 8
A 95% confidence interval for p1 - p2 is shown. What can be concluded?A 95% interval for p1 - p2.
AThere is convincing evidence that p1 is larger, because most of the interval is positive
BThere is not convincing evidence of a difference, because 0 is in the interval
CThere is convincing evidence that p1 and p2 are equal
DThere is convincing evidence of a difference, because the interval is narrow
Question 9
In a test of H0: p = 0.20 versus Ha: p > 0.20, what is a Type I error?
AConcluding p is greater than 0.20 when p is actually 0.20
BConcluding p is 0.20 when p is actually greater than 0.20
CFailing to reject H0 when p is greater than 0.20
DRejecting H0 when the P-value is greater than the significance level
Question 10
Which change increases the power of a significance test for a proportion, if the other factors stay the same?
AIncreasing the sample size
BDecreasing the significance level
CChoosing an alternative value closer to p0
DUsing a smaller sample with the same alpha
🎉 Quiz complete!
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How does this quiz work?
Read each question, choose one answer among A, B, C and D, then check it: a short explanation appears after every answer. Your score out of 10 is shown at the end, and you can restart the quiz as often as you like.
What should you review before the quiz?
Reread the key facts of the lesson and the worked example. If a question is hard, go back to the matching part of the lesson, then try the quiz again. Write your work on scrap paper: most mistakes come from skipping a step, not from the idea itself.
Remember:
Check three conditions: random, 10% (independence), and Large Counts (at least 10 successes and 10 failures).
A one-proportion z interval is the sample proportion plus or minus z* times the standard error; z* is 1.645, 1.960 or 2.576 for 90%, 95% or 99%.
A P-value is computed assuming H0 is true; a small P-value is evidence against H0.
A Type I error has probability alpha; power equals 1 minus the probability of a Type II error.
The sample size for a margin of error ME is n = (z*/ME)^2 p(1-p), rounded up.
How to use this ap statistics proportions quiz
Retake this ap statistics proportions quiz until every answer is right, then move on to the worksheet and the test.
