AP Statistics Unit 4 practice questions
Try 10 multiple-choice questions from Unit 4 here. Pick an answer to see why it's right or wrong, then take the timed test above for a full AP-style set.
Question 1
A biologist measures the length of fish from two independent populations. Population A has a standard deviation of 15 cm, and a random sample of 25 fish is selected. Population B has a standard deviation of 20 cm, and a random sample of 16 fish is selected. What is the standard deviation of the sampling distribution of the difference in sample means (mean A minus mean B)?
Approximately 5.8 cm
Approximately 8.0 cm
Approximately 2.0 cm
Approximately 4.0 cm
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Answer: (A)
Calculating the standard deviation requires adding the variances of the sample means and taking the square root: √((15²/25) + (20²/16)) = √(9 + 25) = √34 ≈ 5.83.
Question 2
A standardized test is administered to two independent groups. Group 1 has a population mean of 100 with a standard deviation of 24, and Group 2 has a population mean of 90 with a standard deviation of 18. Random samples of 36 students are selected from each group. If the observed difference in sample means (Group 1 minus Group 2) is 17.5, what is the z-score for this difference?
z = 1.5
z = 1.1
z = 3.5
z = 7.5
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Answer: (A)
Calculating the z-score requires the expected mean difference (100-90=10) and the standard deviation of the difference (√(24²/36 + 18²/36) = √(16+9) = 5). The z-score is (17.5 - 10) / 5 = 1.5.
Question 3
An agricultural researcher compares the yield of two corn varieties. The variance of the yield for Variety X is 200, and the variance for Variety Y is 450. Random samples of 50 plants of Variety X and 90 plants of Variety Y are selected. What is the standard deviation of the sampling distribution of the difference in sample means?
Approximately 3.0
Approximately 9.0
Approximately 1.0
Approximately 4.2
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Answer: (A)
Calculating the parameter requires dividing each population variance by its sample size, adding them, and taking the square root: √(200/50 + 450/90) = √(4 + 5) = √9 = 3.
Question 4
A statistician plans to estimate the difference between two population means using random samples of size n from each population. If the statistician quadruples the sample size to 4n for both populations, how will the mean and standard deviation of the sampling distribution of the difference in sample means change?
Mean remains constant, standard deviation is halved
Mean remains constant, standard deviation is divided by 4
Mean is halved, standard deviation is halved
Mean remains constant, standard deviation doubles
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Answer: (A)
Quadrupling the sample size divides the variance terms by 4, which results in dividing the standard deviation by √4 = 2. The mean of the sampling distribution is unbiased and does not depend on n.
Question 5
An agronomist compares crop yields from two independent fields, Field A and Field B, to determine if the mean yield of Field A is significantly higher than that of Field B. Which hypotheses should be used for this test?
H₀: μ_A = μ_B and Hₐ: μ_A > μ_B
H₀: μ_A = μ_B and Hₐ: μ_A < μ_B
H₀: μ_A = μ_B and Hₐ: μ_A ≠ μ_B
H₀: x̄_A = x̄_B and Hₐ: x̄_A > x̄_B
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Answer: (A)
Comparing the distributions requires setting the null hypothesis as no difference and the alternative as the specific directional claim (Field A > Field B) using population parameters.
Question 6
A superintendent compares the distributions of reading scores for students using Method X and Method Y to see if there is any difference in the mean scores. Which hypotheses correctly frame this comparison?
H₀: μ_X - μ_Y = 0 and Hₐ: μ_X - μ_Y ≠ 0
H₀: μ_X - μ_Y = 0 and Hₐ: μ_X - μ_Y > 0
H₀: μ_X - μ_Y = 0 and Hₐ: μ_X - μ_Y < 0
H₀: x̄_X - x̄_Y = 0 and Hₐ: x̄_X - x̄_Y ≠ 0
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Answer: (A)
Recognizing the goal is to find 'any difference' requires a two-sided alternative hypothesis (≠) using the difference of population means.
Question 7
A doctor investigates if a new medication results in lower mean cholesterol levels compared to a standard treatment. Which pair of hypotheses correctly tests this claim?
H₀: μ_New = μ_Std and Hₐ: μ_New < μ_Std
H₀: μ_New = μ_Std and Hₐ: μ_New > μ_Std
H₀: μ_New < μ_Std and Hₐ: μ_New = μ_Std
H₀: x̄_New = x̄_Std and Hₐ: x̄_New < x̄_Std
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Answer: (A)
Translating the goal of 'lower mean levels' requires a one-sided alternative hypothesis where the new mean is less than the standard mean.
Question 8
An engineer compares braking distances for two car models. She wants to test the claim that Model A has a shorter mean braking distance than Model B. Which hypotheses are appropriate?
H₀: μ_A - μ_B = 0 and Hₐ: μ_A - μ_B < 0
H₀: μ_A - μ_B = 0 and Hₐ: μ_A - μ_B > 0
H₀: μ_A - μ_B = 0 and Hₐ: μ_A - μ_B ≠ 0
H₀: μ_A - μ_B < 0 and Hₐ: μ_A - μ_B = 0
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Answer: (A)
Testing for a 'shorter' distance implies Model A is less than Model B, so the difference (A - B) in the alternative hypothesis must be less than zero.
Question 9
An economist compares the distribution of annual salaries in Sector 1 and Sector 2 to test if the mean salary in Sector 1 exceeds that of Sector 2. Which hypotheses should be used?
H₀: μ_1 = μ_2 and Hₐ: μ_1 > μ_2
H₀: μ_1 = μ_2 and Hₐ: μ_1 < μ_2
H₀: μ_1 > μ_2 and Hₐ: μ_1 = μ_2
H₀: x̄_1 = x̄_2 and Hₐ: x̄_1 > x̄_2
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Answer: (A)
The term 'exceeds' indicates a directional test where the alternative hypothesis states the mean of Sector 1 is greater than the mean of Sector 2.
Question 10
A researcher tests whether the mean concentration of a pollutant in River North is different from the mean concentration in River South. Which hypotheses correctly represent this test?
H₀: μ_N - μ_S = 0 and Hₐ: μ_N - μ_S ≠ 0
H₀: μ_N - μ_S = 0 and Hₐ: μ_N - μ_S > 0
H₀: μ_N - μ_S = 0 and Hₐ: μ_N - μ_S < 0
H₀: x̄_N - x̄_S = 0 and Hₐ: x̄_N - x̄_S ≠ 0
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Answer: (A)
The phrase 'is different from' implies no specific direction is suspected, requiring a two-sided alternative hypothesis (≠).
What's on the AP Statistics Unit 4 practice test
The standard version takes about 88 minutes and follows the timing and directions of the AP exam, sized to one unit:
- 20 Multiple Choice Questions (43 minutes)
- 1 FRQ – FRQ 2 – Multi-Focus on Practices 3 and 4 (23 minutes)
- 1 FRQ – FRQ 3 – Inference (23 minutes)
Questions are drawn from 3739 multiple-choice questions and 33 FRQs written for Unit 4, Inference for Quantitative Data: Means.
Practice AP Statistics Unit 4 FRQs
Answer the unit's free-response questions one at a time and get a score on every part.
- FRQ 2 – Multi-Focus on Practices 3 and 4 (11 questions)
- FRQ 3 – Inference (12 questions)
- FRQ 4 – Multi-Focus on Practices 2, 3, and 4 (10 questions)
Review Unit 4 before you start
- 4.1 Sampling Distributions for Sample Means
- 4.2 Constructing a Confidence Interval for a Population Mean or Population Mean Difference
- 4.3 Justifying a Claim Based on a Confidence Interval for a Population Mean or Population Mean Difference
- 4.4 Setting Up a Test for a Population Mean or Population Mean Difference
- 4.5 Carrying Out a Test for a Population Mean or Population Mean Difference
- 4.6 Sampling Distributions for the Difference Between Two Sample Means
- 4.7 Constructing a Confidence Interval for the Difference Between Two Population Means
- 4.8 Justifying a Claim Based on a Confidence Interval for the Difference Between Two Population Means
- 4.9 Setting Up a Test for the Difference Between Two Population Means
- 4.10 Carrying Out a Test for the Difference Between Two Population Means
- Unit 4 Overview: Inference for Quantitative Data: Means