AP Statistics Practice Quiz: Constructing a Confidence Interval for a Population Proportion
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Test your understanding with short quizzes. This quiz has 16 questions to check your progress.
Question 1 of 16
All Questions (16)
A) One-sample t-interval for a mean
B) One-sample z-interval for a proportion
C) Two-sample z-test for a proportion
D) Chi-square test for goodness of fit
Correct Answer: B
Content points 1 and 6 state that the appropriate procedure for estimating a single population proportion is a one-sample z-interval for a proportion.
A) The data must be perfectly symmetric and the sample size must be less than 30.
B) The population must be normally distributed and the sample must be a convenience sample.
C) The conditions for independence and approximate normality of the sampling distribution must be met.
D) The population standard deviation must be known and the data must be quantitative.
Correct Answer: C
Content point 7 explicitly states that to calculate a confidence interval for a population proportion, one must check for independence and the approximate normality of the sampling distribution.
A) Margin of error ± point estimate
B) Point estimate ± standard error
C) Point estimate ± margin of error
D) Critical value ± standard deviation
Correct Answer: C
Content point 12 states that an interval estimate is constructed as 'point estimate ± margin of error.'
A) The exact difference between the sample proportion and the population proportion.
B) The probability that the confidence interval is incorrect.
C) An indication of how much the sample statistic is likely to vary from the population parameter.
D) The standard deviation of the population.
Correct Answer: C
According to content point 9, a margin of error indicates how much a sample statistic is likely to vary from the population parameter.
A) The sample proportion and the sample size.
B) The point estimate and the standard deviation.
C) The critical value (z*) and the standard error (SE).
D) The confidence level and the sample size.
Correct Answer: C
Content point 10 specifies that for categorical variables, the margin of error is the critical value (z*) times the standard error (SE).
A) The true standard deviation of the population.
B) An estimate of the standard deviation of the statistic.
C) The range of the sample data.
D) The same as the margin of error.
Correct Answer: B
Content point 8 defines the standard error of a statistic as an estimate of its standard deviation.
A) It is the sample proportion calculated from the data.
B) It represents the standard deviation of the sample.
C) It defines the boundaries for the middle C% of the standard normal distribution.
D) It is the minimum sample size required for the interval.
Correct Answer: C
Content point 13 defines critical values (z*) as the boundaries for the middle C% of the standard normal distribution, where C corresponds to the confidence level.
A) Decrease the sample size.
B) Increase the sample size.
C) Use a t-distribution instead of a z-distribution.
D) Use a smaller estimate for the sample proportion.
Correct Answer: B
Content points 3 and 11 describe the relationship between margin of error and sample size. To decrease the margin of error, one must increase the sample size (n), as n is in the denominator of the margin of error formula.
A) Conduct a small pilot study to find the exact population proportion.
B) Solve the margin of error formula for the sample size, n.
C) Use the formula n = z* / SE.
D) The sample size must always be at least 10% of the population.
Correct Answer: B
Content point 11 states that the margin of error formula can be solved for n to find the minimum sample size required for a given margin of error.
A) The proportion of students in the sample who own a laptop.
B) The proportion of all students in the population who own a laptop.
C) The probability that a randomly selected student owns a laptop.
D) The number of students in the population who own a laptop.
Correct Answer: B
Content point 4 states that the procedure is to calculate an appropriate confidence interval for a *population proportion*. Therefore, the interval (0.78, 0.86) is an estimate for the proportion in the entire population, not just the sample.
A) (20, 60)
B) (100, 300)
C) (1,000, 3,000)
D) (2,000, 6,000)
Correct Answer: C
Based on content points 5 and 14, the interval estimate with specified units is found by multiplying the interval bounds by the total population size. Lower bound: 0.02 * 50,000 = 1,000. Upper bound: 0.06 * 50,000 = 3,000. The interval is (1,000, 3,000).
A) population from which the sample was drawn is normally distributed.
B) sample data itself follows a normal distribution.
C) sampling distribution of the sample proportion is approximately normal.
D) sample size is larger than the population size.
Correct Answer: C
Content point 7 specifies that the check for approximate normality applies to the *sampling distribution*, not the population or the sample itself. This allows for the use of the normal model and z* critical values.
A) 0.05
B) 0.10
C) 0.55
D) 0.60
Correct Answer: D
According to content point 12, the interval is constructed as 'point estimate ± margin of error.' The point estimate is the center of the interval. The center of (0.55, 0.65) is (0.55 + 0.65) / 2 = 0.60.
A) 0.08
B) 0.16
C) 0.50
D) 0.58
Correct Answer: A
The interval is 'point estimate ± margin of error' (Content 12). The full width of the interval is 0.58 - 0.42 = 0.16. The margin of error is half the width of the interval, which is 0.16 / 2 = 0.08. This value indicates how much the sample statistic is likely to vary from the population parameter (Content 9).
A) A quantitative variable with a known population standard deviation.
B) A categorical variable.
C) A quantitative variable with an unknown population standard deviation.
D) A paired quantitative variable.
Correct Answer: B
Content point 1 specifies that this procedure is for a population *proportion*. Proportions are calculated from categorical data (e.g., success/failure, yes/no). Content point 10 confirms this by referring to categorical variables.
A) 0.05, as it is the standard significance level.
B) 0.50, as it produces the maximum possible standard error.
C) 1.00, as it represents certainty.
D) 0.10, as it satisfies the 10% condition.
Correct Answer: B
This question synthesizes concepts from content points 3, 10, and 11. The margin of error is z* times the standard error. The standard error for a proportion includes the term p-hat*(1-p-hat). This term is maximized when p-hat = 0.50. Using this value yields the most conservative (largest) estimate for the required sample size, guaranteeing the desired margin of error will be met or bettered.