AP Statistics · Topic 5.7
Sampling Distributions for Sample Means Practice
Part of Sampling Distributions.(UNC-3.H)
Practice questions
50
Sample questions
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Sample 1difficulty 1/5
A population has a known mean μ and known standard deviation σ. Random samples of size n are repeatedly drawn.
The mean of the sampling distribution of x̄ is always equal to which of the following?
- A
x̄ from any one sample.
- B
- Ccheck_circle
μ (the population mean).
- D
μ/n.
Why
The sample mean is unbiased, so μ_x̄ = μ.
- A
Sample 2difficulty 2/5
A population has σ = 30. Samples of n = 100 are taken.
The standard deviation of x̄ is:
- A
30
- B
0.3
- Ccheck_circle
3
- D
300
Why
σ_x̄ = 30/√100 = 30/10 = 3.
- A
Sample 3difficulty 2/5
Which best describes the term "standard error" of x̄?
- A
Always equal to σ/√n.
- B
The bias of x̄.
- C
The mean of x̄.
- Dcheck_circle
An estimate of σ_x̄ when σ is unknown, using s/√n.
Why
The SE of x̄ is the estimated SD using the sample SD: s/√n.
- A
Sample 4difficulty 2/5
Why is x̄ called an unbiased estimator of μ?
- A
Because s = σ.
- Bcheck_circle
Because the mean of its sampling distribution equals μ.
- C
Because every sample gives x̄ = μ.
- D
Because the median equals μ.
Why
Unbiased means E(x̄) = μ_x̄ = μ.
- A
Sample 5difficulty 2/5
Two simulated sampling distributions of x̄ are overlaid on the same axes.
Two sampling distributions of x̄ have the same mean μ but different SDs. Which has a smaller σ?
- A
Cannot tell.
- Bcheck_circle
The taller, narrower one (larger n).
- C
Both have the same SD.
- D
The wider one (smaller n).
Why
A narrower sampling distribution corresponds to a smaller σ_x̄ = σ/√n, which occurs with larger n.
- A