Worksheet titled "Bias and Sampling Worksheet" featuring seven multiple-choice questions related to statistical sampling techniques and unbiased sample selection.

Let’s go through each question one by one, step by step. We’ll think about what each sampling method means and which one fits the situation best.

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Question 1:
A large corporation wants to find out which benefits plan its employees would prefer. Which procedure would be most likely to obtain a statistically unbiased sample?

- Unbiased = every employee has an equal chance of being picked.
- Option a: survey a random sample from a list of all employees → this gives everyone a fair chance. Good!
- Option b: invite all to email choices → only people who care enough will respond → biased.
- Option c: suggestion boxes in random locations → not everyone goes there → biased.
- Option d: pick one person per department → might miss differences within departments → not fully random.

✔ Best answer: a

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Question 2:
University polled 500 students, randomly selecting them proportional to number enrolled in each degree program.

- “Proportional to each group” → that’s stratified sampling (divide into groups, then sample from each).
- Simple random = just pick any 500 without regard to programs.
- Systematic = every nth person.
- Convenience = easy-to-reach people.
- Voluntary = they choose to respond.

✔ Best answer: b. stratified

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Question 3:
Telemarketing firm randomly selected 1000 names from store’s database and contacted them.

- Randomly selected from entire list → simple random sampling.
- Not divided into groups → not stratified.
- Not every nth → not systematic.
- They were contacted, didn’t volunteer → not voluntary response.
- Not based on convenience → not convenience.

✔ Best answer: a. simple random

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Question 4:
Readers of car magazine asked to mail answers to survey.

- Only readers who want to respond will do it → voluntary response.
- Not random, not stratified, not systematic, not convenience (it’s not about location or ease — it’s about willingness).

✔ Best answer: e. voluntary response

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Question 5:
Random starting point, then every nth individual.

- That’s the definition of systematic random sampling.
- Simple random = no pattern.
- Cluster = pick whole groups.
- Stratified = divide then sample from each group.

✔ Best answer: d. systematic random sampling

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Question 6:
Systematic random sampling used to interview residents in 25% of 80 apartments. Sampling interval?

- Total apartments = 80
- Want 25% → 25% of 80 = 0.25 × 80 = 20 apartments to sample.
- In systematic sampling, interval = total population / sample size = 80 / 20 = 4.
- So you pick every 4th apartment after a random start.

✔ Best answer: a. 4

*(Double-check: If you pick every 4th, you get 80 ÷ 4 = 20 people → yes, 25%. Correct.)*

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Question 7:
Simple random sample of 200 people selected from 1230 male students in psychology course. What is the population?

- Population = the entire group we’re studying.
- Here, we’re sampling from the 1230 male students → so that’s the population.
- The 200 are the sample.
- “People taking part in test” = sample.
- “Male students enrolled...” = population.

✔ Best answer: b. 1230

Wait — let’s read carefully:
“The population being considered is”

Option b says “1230” — that’s the number, but technically the population is the *group*, not the number. But looking at options:

a. 200 → sample size
b. 1230 → size of population
c. people taking part → sample
d. male students enrolled... → actual population description

Hmm… option d describes the population correctly: “male students enrolled in a university psychology course”

But option b is just the number. Usually, “population” refers to the group, not the count. However, sometimes questions use “population” to mean the size.

Looking back at question: “The population being considered is”

In statistics, when we say “the population”, we usually mean the group. But here, option d is the full description, while b is just the number.

Actually, re-read:
“A simple random sample of 200 people is selected from the 1230 male students...”

So the population is the 1230 male students → so the population size is 1230, but the population itself is those students.

But look at the options:

a. 200 → no, that’s sample
b. 1230 → this is the size of the population
c. people taking part → sample
d. male students enrolled... → this is the actual population group

I think the question is asking for the population as a group, so d is correct.

Wait — let me check standard terminology.

In many textbooks, if they say “what is the population?”, and give options like numbers vs descriptions, they expect the description.

Example: If I say “I sampled 100 voters from 1000 registered voters in town X”, the population is “registered voters in town X”, not “1000”.

So here, population = male students enrolled in the course → option d.

But why is option b there? Maybe to trick.

Actually, let’s see the exact wording: “The population being considered is”

And option d says: “male students enrolled in a university psychology course” — that matches exactly.

Option b is just “1230” — which is N, the population size.

I think the intended answer is d, because population refers to the group, not the number.

But wait — in some contexts, especially multiple choice, they might accept the number. Let me think again.

No — in statistics education, when asked “what is the population?”, they want the group. For example, AP Stats questions always distinguish between population (group) and parameter (number describing group).

Here, since option d precisely describes the group, and b is just a number, d is better.

But let me confirm with logic: if I say “the population is 1230”, that doesn’t make sense — 1230 what? It’s incomplete. Whereas “male students enrolled...” is complete.

So ✔ Final decision: d

Wait — I recall now: in some worksheets, they might list the size as “population” meaning population size. But strictly speaking, population is the set.

Looking at the other questions, they are testing understanding of terms.

Actually, let’s see question 7 again:
“A simple random sample of 200 people is selected from the 1230 male students... The population being considered is”

The phrase “being considered” suggests the group under study, which is the 1230 male students → so the population is those students, i.e., option d.

Yes, I think d is correct.

But earlier I thought b — let me double-check online or standard definition.

Upon second thought: in many introductory stats materials, when they say “identify the population”, and give options including the size and the description, they expect the description.

For example, from Khan Academy: “The population is the entire group that you want to draw conclusions about.”

Here, we want to draw conclusions about the male students in the course → so population is them → option d.

Option b is the population size, not the population.

So ✔ Answer: d

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Now, compiling all answers:

1. a
2. b
3. a
4. e
5. d
6. a
7. d

Final Answer:
1. a
2. b
3. a
4. e
5. d
6. a
7. d