AP Statistics Flashcards: Sampling Distributions for 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 allows us to assume the sampling distribution of p-hat is approximately normal?
The sampling distribution of p-hat can be described as approximately normal if the Large Counts Condition (np >= 10 and n(1-p) >= 10) is met.
Card 1 of 11
All Flashcards (11)
What condition allows us to assume the sampling distribution of p-hat is approximately normal?
The sampling distribution of p-hat can be described as approximately normal if the Large Counts Condition (np >= 10 and n(1-p) >= 10) is met.
What is the mean of the sampling distribution of a sample proportion, p-hat?
The mean of the sampling distribution of p-hat is equal to the true population proportion, p.
What are the two key parameters that define the sampling distribution for a sample proportion?
The two key parameters are the mean, which equals p, and the standard deviation, which equals sqrt(p(1-p)/n).
When sampling without replacement, what condition must be met for the standard deviation formula for a sample proportion to be approximately correct?
If sampling without replacement, the sample size must be less than 10% of the population size for the standard deviation formula to be considered accurate.
What is the Large Counts Condition?
The Large Counts Condition states that for the sampling distribution of p-hat to be approximately normal, both np and n(1-p) must be greater than or equal to 10.
Why is it important to interpret probabilities and parameters for a sampling distribution in context?
Interpreting probabilities and parameters in context is essential for relating the numerical results of the sampling distribution back to the real-world situation being studied.
What is the formula for the standard deviation of the sampling distribution of a sample proportion, p-hat?
The standard deviation of the sampling distribution of p-hat is calculated as sqrt(p(1-p)/n).
From a population of 800 employees, a sample of 100 is taken to estimate the proportion who are satisfied with their benefits. Does this meet the condition for using the standard deviation formula?
No, the condition is not met. The sample size of 100 is greater than 10% of the population (800 * 0.10 = 80), so the standard deviation formula is not approximately correct.
What does the 10% condition ensure when calculating the standard deviation of a sampling distribution for a proportion?
It ensures that when sampling without replacement, the individual selections are approximately independent, making the standard deviation formula valid.
If the true proportion of students who own a car is 0.3, can we assume the sampling distribution of p-hat is approximately normal for a sample of 30 students?
No, because the Large Counts Condition is not met. The value of np is 30(0.3) = 9, which is not greater than or equal to 10.
A factory produces a large number of bolts, and the true proportion of defective bolts is p=0.08. If a sample of 200 bolts is taken, what are the parameters of the sampling distribution of p-hat?
The mean of the sampling distribution is p = 0.08, and the standard deviation is sqrt(0.08(1-0.08)/200), which is approximately 0.019.