AP Statistics · Topic 5.5
Sampling Distributions for Sample Proportions Practice
Part of Sampling Distributions.(UNC-3.F)
Practice questions
32
Sample questions
5 of 32 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 1/5
Why do we check the 10% condition (n ≤ 0.10N) when sampling without replacement?
- A
So that the sample is unbiased.
- B
So that the population is normal.
- Ccheck_circle
So that observations are approximately independent and the SD formula remains valid.
- D
So that p̂ equals p.
Why
With independence ensured by the 10% rule, σ_x̄ = σ/√n and σ_p̂ formulas are valid.
- A
Sample 2difficulty 1/5
Which symbol denotes the sample proportion?
- A
π
- B
p
- Ccheck_circle
p̂
- D
P̄
Why
p̂ (read "p-hat") is the sample proportion.
- A
Sample 3difficulty 1/5
A population has true proportion p = 0.40. Random samples of size n = 100 are taken.
What is the mean of the sampling distribution of p̂?
- A
0.04
- B
0.60
- C
40
- Dcheck_circle
0.40
Why
The mean of the sampling distribution of p̂ equals the population proportion p. So μ_p̂ = 0.40.
- A
Sample 4difficulty 2/5
A random sample of n = 200 students is taken from a large university where 30% have a campus job.
Which statement best describes the sampling distribution of p̂?
- Acheck_circle
Approximately normal because np = 60 ≥ 10 and n(1-p) = 140 ≥ 10.
- B
Cannot be determined without σ.
- C
Exactly normal because the population is large.
- D
Skewed right because p < 0.5.
Why
Large Counts is satisfied (60 ≥ 10 and 140 ≥ 10), so p̂ is approximately normal.
- A
Sample 5difficulty 2/5
A pollster is comparing samples drawn at different sizes from a population with proportion p.
If n is multiplied by 4, the standard deviation σ_p̂ is multiplied by what factor?
- Acheck_circle
1/2
- B
1/4
- C
2
- D
4
Why
σ_p̂ = √(p(1−p)/n). Multiplying n by 4 multiplies the SD by 1/√4 = 1/2.
- A