AP®︎ Statistics: Topic 3.2 Flashcards

Master key terms and definitions for Topic 3.2 of AP Statistics – Sampling Distributions for Sample Proportions to help you prep for quizzes and the AP exam.

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Term

Population Proportion (p)

Definition

The proportion of individuals in the population with the specified characteristic; a fixed parameter

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Population Proportion (p)
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The proportion of individuals in the population with the specified characteristic; a fixed parameter

3.2.A3.2.A.1
Sample Proportion (p̂)
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p̂ = X/n, where X is the number of successes in the sample

3.2.A3.2.A.1
Sampling Distribution of p̂
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The probability distribution of p̂ over all possible random samples of the same size n

3.2.A3.2.A.1
Mean of the Sampling Distribution of p̂
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μ_p̂ = p

3.2.A3.2.A.1
Standard Deviation of the Sampling Distribution of p̂
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σ_p̂ = √(p(1 − p)/n) when sampled observations are independent

3.2.A3.2.A.1
Randomization Condition
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Data should be collected using a random sample from the population

3.2.B3.2.B.1.i
10% Condition
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When sampling without replacement, N ≥ 10n (equivalently, n ≤ 0.10N) so sampled observations can be treated as approximately independent

3.2.B3.2.B.1.ii
Approximate Normal Model for p̂
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If the randomization, 10%, and Large Counts conditions are met, p̂ is approximately N(p, √(p(1 − p)/n))

3.2.B3.2.B.2
Standardizing a Sample Proportion
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z = (p̂ − p)/√(p(1 − p)/n)

3.2.C3.2.C.1
Interpretation of μ_p̂
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Over many random samples of size n, the average sample proportion with the specified characteristic is p

3.2.C3.2.C.1
Interpretation of σ_p̂
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For random samples of size n, p̂ will typically differ from p by about σ_p̂

3.2.C3.2.C.1
Interpretation of a Probability for p̂
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The probability is the proportion of repeated random samples of size n that produce a sample proportion in the stated range, assuming the given population proportion

3.2.C3.2.C.1
Normality Condition / Large Counts Condition
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Approximate normality for p̂ requires np ≥ 10 and n(1 − p) ≥ 10

3.2.B3.2.B.2
Success
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The outcome being counted for a binary categorical variable; just a label, not necessarily a desirable result

3.2.A
Failure
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The outcome not counted for a binary categorical variable

3.2.A
Independence
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Sampled observations must be independent for σ_p̂ = √(p(1 − p)/n) to apply; without replacement, use the 10% condition to justify approximate independence

3.2.B3.2.B.1