AP Statistics Flashcards: Sampling Distributions for Differences in Sample Means
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 14 cards to help you master important concepts.
A sample of size 50 is taken from a skewed population A, and a sample of size 40 is taken from a normal population B. Is the sampling distribution of (x̄ₐ - x̄ᵦ) approximately normal?
Yes, the sampling distribution is approximately normal because both sample sizes are large enough (n₁ ≥ 30 and n₂ ≥ 30), satisfying the Central Limit Theorem.
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A sample of size 50 is taken from a skewed population A, and a sample of size 40 is taken from a normal population B. Is the sampling distribution of (x̄ₐ - x̄ᵦ) approximately normal?
Yes, the sampling distribution is approximately normal because both sample sizes are large enough (n₁ ≥ 30 and n₂ ≥ 30), satisfying the Central Limit Theorem.
If the mean height of adult men is 70 inches and for women is 65 inches, what is the mean of the sampling distribution of the difference in sample means (men - women)?
The mean of the sampling distribution is the difference in population means, so it would be μ_men - μ_women = 70 - 65 = 5 inches.
A sample of size 20 is taken from a normal population, and a sample of size 25 is taken from an unknown population. Can we assume the sampling distribution of the difference in means is normal?
No, we cannot assume normality because one of the populations has an unknown distribution and its sample size (n=25) is not large enough (n<30).
If the population distributions are not normal, how can the sampling distribution of the difference in means be approximately normal?
If the population distributions are not normal, the sampling distribution is approximately normal if both sample sizes are large enough (e.g., n₁ ≥ 30 and n₂ ≥ 30) due to the Central Limit Theorem.
How do you interpret the mean of the sampling distribution, μ₁ - μ₂, in context?
This parameter represents the true difference in the means between the two populations from which samples are being drawn.
How should a calculated probability from a sampling distribution for a difference of sample means be interpreted?
The probability should be interpreted in context as the likelihood of observing a difference in sample means as extreme or more extreme than the one found, assuming a certain true difference in population means.
Under what condition is the standard deviation formula for the difference in sample means considered approximately correct when sampling without replacement?
The formula is approximately correct if both sample sizes are less than 10% of their respective population sizes (the 10% condition).
What is the formula for the standard deviation of the sampling distribution of the difference in sample means?
The standard deviation is calculated using the formula √(σ₁²/n₁ + σ₂²/n₂), provided the samples are independent.
When is the sampling distribution of the difference in means guaranteed to be normal?
The sampling distribution of the difference in means is guaranteed to be normal if both of the original population distributions are normal.
Why is it important that parameters for a sampling distribution for a difference of sample means be interpreted in context?
Interpreting parameters in context connects the statistical calculations to the real-world problem, explaining what the numbers mean regarding the populations being studied.
What is the mean of the sampling distribution of the difference in sample means (x̄₁ - x̄₂)?
The mean of the sampling distribution of the difference in sample means is equal to the difference in the population means, μ₁ - μ₂.
What are the two main parameters of a sampling distribution for a difference in sample means?
The two main parameters are the mean, which is μ₁ - μ₂, and the standard deviation, which is calculated from the population variances and sample sizes.
What is the 'Normal/Large' condition for the difference in sample means?
This condition checks whether the sampling distribution can be modeled as approximately normal; it is met if both populations are normal OR if both sample sizes are 30 or greater.
What does the standard deviation of the sampling distribution for a difference in sample means measure?
It measures the typical distance of the observed difference in sample means (x̄₁ - x̄₂) from the true difference in population means (μ₁ - μ₂).