Designing Studies: Sampling and Experimental Design — HS Statistics practice questions

Researchers compare the health of people who already choose to exercise with people who do not. This is:

1. a randomized experiment
2. a matched-pairs experiment
3. an observational study
4. a census

Answer: C — an observational study

C) Correct — The researchers do not assign the exercise. A) Subjects chose their own exercise habits. B) No treatment is assigned at all. D) Not everyone in the population is measured.

A website asks visitors to vote in an online poll. The main problem is:

1. voluntary response bias
2. response bias from a leading question
3. nonresponse bias
4. no bias, because anyone can vote

Answer: A — voluntary response bias

A) Correct — People with strong opinions are the most likely to respond. B) Nothing here says the question is worded unfairly. C) That happens when chosen people do not answer; here no one was chosen. D) Letting people choose themselves is what creates the bias.

The purpose of a control group is to:

1. provide a baseline for comparison
2. receive the strongest dose
3. avoid being measured
4. remove the placebo effect entirely

Answer: A — provide a baseline for comparison

A) Correct — It shows what happens without the treatment. B) The control group gets no treatment or a placebo. C) It is measured just like the treatment group. D) A placebo group lets you measure that effect; nothing removes it.

Each runner tries both shoe A and shoe B, in random order. This is a:

1. matched-pairs design
2. completely randomized design
3. block design with three blocks
4. observational study

Answer: A — matched-pairs design

A) Correct — Each subject serves as their own comparison. B) Would give each runner only one shoe. C) There are no separate blocks here. D) The researchers assign the shoes.

A simple random sample of size n is one in which:

1. the researcher picks people who seem typical
2. the first n people who respond are used
3. each subgroup is sampled separately
4. every group of n individuals has the same chance of being chosen

Answer: D — every group of n individuals has the same chance of being chosen

D) Correct — That is what makes it simple and random. A) Personal choice introduces bias. B) Is a convenience or voluntary sample. C) Describes a stratified sample.

Nonresponse vs voluntary response bias?

Nonresponse: people who were chosen do not respond. Voluntary response: people choose themselves (call-ins, online polls), so those with strong opinions are overrepresented.

Population vs sample?

Population: all members. Sample: subset used to study population.

Placebo?

Inert treatment. Subjects can show effects from belief alone.

What should you check before trusting a statistical claim?

Sample size, methodology, source bias, confounders, statistical vs practical significance.