Module 04 Knowledge Check
5 questions. Pass mark 4 out of 5. Answer every question before checking the answer key below, then retry after reading the feedback.
1. Five samples of 30 from one population give five different means because…
- A. one of them is wrong
- B. sampling varies; none is wrong
- C. the population changed
- D. the seed was not set
2. As n grows, the sampling distribution of the mean from a skewed population…
- A. stays skewed
- B. becomes approximately normal and narrower
- C. becomes wider
- D. matches the population shape
3. Standard error differs from standard deviation in that it…
- A. describes the spread of values
- B. describes the spread of the estimate and falls with n
- C. is always larger
- D. requires a normal population
4. Bootstrapping requires rng.choice(..., replace=True) because…
- A. it is faster
- B. without replacement every resample is a reordering with the same mean
- C. it avoids bias
- D. it needs more data
5. For a proportion, the preferred interval method is…
- A. the normal approximation
- B. Wilson
- C. the bootstrap only
- D. there is no difference
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Answer Key and Explanations
Check these only after attempting every question.
1. B — sampling varies; none is wrong
Variation between samples is not error. Its spread is the quantity inference measures.
2. B — becomes approximately normal and narrower
At n = 200 the exponential population's sample means had an SD of 3.44 against 22.42 at n = 5.
3. B — describes the spread of the estimate and falls with n
SD = 112.82 described the data; SE = 20.60 described how precisely the mean was known.
4. B — without replacement every resample is a reordering with the same mean
Resampling without replacement reports zero uncertainty.
5. B — Wilson
The normal approximation misbehaves badly at small n and at proportions near 0 or 1, sometimes leaving [0, 1] entirely.
Practical Check
Apply this module to your own work: complete the module activity for *Simulation, Bootstrap, and Confidence Intervals*, then write one sentence naming what your result shows and one naming what it does not.
Strong Answer Pattern
A strong answer names the task, the evidence used, the check performed, and the remaining limitation. It avoids "proved", "guaranteed", or "always" unless the evidence genuinely supports it.