AP Statistics Flashcards: Sampling Distributions for Differences in Sample Proportions
Written by AP Content Team, Verified for 2026 AP Exams, Last updated: May 2026
Review key ideas with interactive flashcards. This set includes 11 cards to help you master important concepts.
What condition must be met to use the standard deviation formula for a difference in proportions when sampling without replacement?
The 10% condition must be met, meaning both sample sizes must be less than 10% of their respective populations to ensure the formula is approximately correct.
Card 1 of 11
All Flashcards (11)
What condition must be met to use the standard deviation formula for a difference in proportions when sampling without replacement?
The 10% condition must be met, meaning both sample sizes must be less than 10% of their respective populations to ensure the formula is approximately correct.
What are the parameters of a sampling distribution for a difference in sample proportions?
The parameters are the mean, which is p₁ - p₂, and the standard deviation, which is calculated using a specific formula involving both population proportions and sample sizes.
How do you determine if the sampling distribution for a difference of sample proportions can be described as approximately normal?
The sampling distribution is approximately normal if the Large Counts Condition is met for both samples.
What is the formula for the standard deviation of the sampling distribution of the difference in sample proportions?
The standard deviation is calculated using the formula: √[(p₁(1-p₁)/n₁) + (p₂(1-p₂)/n₂)].
What is the mean of the sampling distribution of the difference in sample proportions (p̂₁ - p̂₂)?
The mean of the sampling distribution of the difference in sample proportions is the difference between the true population proportions, p₁ - p₂.
How should the parameters for a sampling distribution for a difference of proportions be interpreted?
The parameters, such as the mean (p₁ - p₂), should always be interpreted in the context of the specific populations being compared.
What does the Large Counts Condition confirm for the sampling distribution of the difference in sample proportions?
Meeting the Large Counts Condition for both samples confirms that the shape of the sampling distribution of the difference in proportions is approximately normal.
Define the Large Counts Condition in the context of a difference in sample proportions.
The Large Counts Condition is met if the number of expected successes and failures (e.g., n₁p₁, n₁(1-p₁)) are all at least 10 for both samples.
If you are told a sampling distribution for a difference in proportions is approximately normal, what can you infer?
You can infer that the Large Counts Condition has been met for both of the samples from which the proportions were calculated.
When asked to interpret a probability related to the difference in sample proportions, what key element must be included?
The interpretation must be given in the context of the problem, clearly stating what the probability represents for the difference between the two specific groups.
Why is it important that sample sizes are less than 10% of their populations when dealing with differences in proportions?
This condition ensures the independence of observations when sampling without replacement, which validates the use of the standard deviation formula.