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 resampling…
- A. without replacement
- B. with replacement, at the original sample size
- C. with replacement, at twice the sample size
- D. from the population
5. '95% confidence' is a property of…
- A. this particular interval
- B. the procedure, across repeated samples
- C. the data's spread
- D. the sample size
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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 were symmetric with an SD of 3.51, against 22.80 at n = 5.
3. B — describes the spread of the estimate and falls with n
SD = 95.75 described the data; SE = 17.48 described how precisely the mean was known.
4. B — with replacement, at the original sample size
Without replacement you just reorder the same values and every resample has an identical mean.
5. B — the procedure, across repeated samples
Of 1000 intervals, 947 contained the truth. Any one of them either does or does not.
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.