Multiple choice questions on bias and sampling techniques in statistical surveys.

Explanation:
Let’s go through each question one by one and choose the best answer with reasoning.

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?
- a. Survey a random sample of employees from a list of all employees → This is random sampling, which avoids bias if done properly.
- b. Invite all employees to indicate choices by e-mail → This is voluntary response; only those motivated will respond → biased.
- c. Place suggestion boxes at random locations → Not random for *people*; people who pass by or are in certain departments may dominate → biased.
- d. Assemble a group with one member from each department → This is *stratified* if done carefully, but “one member from each department” doesn’t guarantee randomness within departments, and small departments may be overrepresented. Still, it’s better than convenience or voluntary, but not as good as true random sampling.
✔ Best: a — simple random sampling gives the most unbiased result.

2. A university polled 500 of its students, randomly selecting them proportional to the number of students enrolled in each degree program. Classify the sampling method.
- Proportional to size of groups (degree programs) → this is stratified sampling, where the population is divided into strata (degree programs), and samples are taken proportionally from each.
✔ Answer: b. stratified

3. A telemarketing firm randomly selected 1000 names from a store’s database and contacted them. Classify the sampling method.
- Random selection from a list (database) → no grouping, no system, just random draw → simple random sampling.
Note: Even though it’s a database, if it's truly random and every name had equal chance, it’s simple random.
✔ Answer: a. simple random

4. Readers of a car magazine were asked to mail in their answers to a survey. Classify this.
- Only those who choose to respond do so → voluntary response → highly biased (e.g., only passionate fans reply).
✔ Answer: e. voluntary response

5. When a random starting point is chosen, followed by every *n*th individual, this sampling method is…
- That’s the definition of systematic random sampling.
Example: Pick random start between 1–10, then pick every 10th person after that.
✔ Answer: a. simple random sampling? Wait — no!
Let’s double-check:
- Simple random = each person has equal chance, selected independently (like drawing names from a hat).
- Systematic = fixed interval after random start.
So correct is: d. systematic random sampling
(Note: sometimes called just “systematic sampling”, but option says “systematic random sampling” — that’s the right match.)
✔ Answer: d

6. Systematic random sampling is used to interview residents in 25% of 80 apartments in a building. The sampling interval would be?
- Total population = 80 apartments
- Want 25% → 0.25 × 80 = 20 apartments to sample
- In systematic sampling, sampling interval *k* = N / n = total / sample size = 80 / 20 = 4
So you pick a random start (1–4), then every 4th apartment after that.
✔ Answer: a. 4

7. A simple random sample of 200 people is selected from the 1230 male students in a university psychology course to take part in a psychological test. The population being considered is…
- They’re sampling *from* the 1230 male students → that group is the population.
- The sample is 200, but the population is the full group they drew from.
So: male students enrolled in a university psychology course
✔ Answer: d

Now let’s list all answers clearly:

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