Sampling, Simulation & Inference — Drills
Sampling, Simulation & Inference has 5 drill skills. Each one generates fresh questions every time, with a hint and full worked steps, so you can keep practising a single skill until it settles.
What these drills cover
These questions use 10 ideas from the course. Follow any of them for a definition, where it is taught, and what it leads to.
- Percent — Parts per hundred. 37% = 37100 = 0.37.
- Repeating — Every fraction becomes a decimal that either stops or repeats forever.
- Random sample — Every member has an equal chance of being picked — the only kind you can trust.
- Mean — Two kinds of centre: the balance point, and the middle value.
- Square root — For k ≥ 0, √k is the nonnegative number whose square is k.
- Factor — A number that divides evenly into another.
- Range — The set of outputs that actually occur.
- Association — A pattern linking the two variables.
- Bias — A flaw in how the sample was gathered that tilts the result in one direction.
- Margin of error — How far the sample result might sit from the truth.
Margin
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
Using the conservative 95% shortcut, estimate the margin of error for a simple random sample of 400. Give a percent rounded to the nearest tenth.
Worked answer
5
√400=20
120 ≈ 5%
Problem 2
Using the conservative 95% shortcut, estimate the margin of error for a simple random sample of 900. Give a percent rounded to the nearest tenth.
Worked answer
3.3
√900=30
130 ≈ 3.3%
Size
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
About what sample size gives a margin of error of 10%?
Worked answer
100
√n = 10
n=100
Problem 2
About what sample size gives a margin of error of 1%?
Worked answer
10000
√n = 100
n=10000
Interval
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A poll reports 51% with a margin of error of 4%. Give the upper end of the interval, as a percent.
Worked answer
55
51 + 4 = 55
Problem 2
A poll reports 58% with a margin of error of 3%. Give the lower end of the interval, as a percent.
Worked answer
55
58 - 3 = 55
Decided
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
A poll gives 55% with a margin of 3%. Does the interval establish a lead over 50%? Answer yes or no.
Worked answer
yes
The interval is 52% to 58%
It sits entirely above 50%, so yes
Problem 2
A poll gives 49% with a margin of 3%. Does the interval establish a lead over 50%? Answer yes or no.
Worked answer
no
The interval is 46% to 52%
It contains 50%, so the data has not decided
Quadruple
Unlimited questions of this kind are generated in the app. Two examples:
Problem 1
To divide a margin of error by 2, by what factor must the sample size grow?
Worked answer
4
√n must grow by 2
So n grows by 22 = 4
Problem 2
To divide a margin of error by 3, by what factor must the sample size grow?
Worked answer
9
√n must grow by 3
So n grows by 32 = 9