Q: A researcher divides a population of 1,000 students into four strata based on year (freshman, sophomore, junior, senior) with sizes 300, 200, 400, and 100, respectively. If a sample of 20 students is to be taken using stratified random sampling with proportional allocation, how many students should be sampled from the junior stratum?

$$20 \times \frac{400}{1000} = 8$$

Question 1

Which of the following best describes a simple random sample?

Accepted Answer

A sample in which every possible sample of the same size has the same chance of being chosen.

Question 2

A pharmaceutical company wants to test a new drug. They randomly assign 200 patients to receive the drug and 200 to receive a placebo, without telling either the patients or the administering doctors which group they are in. What is this experimental design called?

Accepted Answer

Double-blind experiment

Question 3

Which of the following statements is TRUE regarding observational studies and experiments?

Accepted Answer

Experiments can establish causation, while observational studies can only reveal association.

Question 4

A researcher divides a population of 1,000 students into four strata based on year (freshman, sophomore, junior, senior) with sizes 300, 200, 400, and 100, respectively. If a sample of 20 students is to be taken using stratified random sampling with proportional allocation, how many students should be sampled from the junior stratum?

Accepted Answer

$$20 	imes \frac{400}{1000} = 8$$

Question 5

Which sampling method is most likely to introduce bias due to ease of data collection rather than randomness?

Accepted Answer

Convenience sampling

Question 6

A hospital administrator wants to survey patient satisfaction. She divides the hospital into five departments and randomly selects all patients from two of these departments. Which sampling method is being used?

Accepted Answer

Cluster sampling

Question 7

In a clinical trial, what is the main purpose of using a placebo?

Accepted Answer

To control for the placebo effect, where subjects report improvement due to expectations rather than the treatment.

Question 8

Which of the following is an example of systematic sampling?

Accepted Answer

Selecting every 5th person from a list after a random starting point.

Question 9

A study follows 10,000 people for 10 years, recording their dietary habits and health outcomes, but does not assign any treatments. What type of study is this?

Accepted Answer

Observational study

Question 10

Why is replication important in experimental design?

Accepted Answer

It allows researchers to see the effects of treatments across a large enough sample to draw valid conclusions.

Question 11

A pollster wants to estimate the proportion of voters who support a new policy. She divides the city into neighborhoods, randomly selects some neighborhoods, and surveys every adult in those neighborhoods. What sampling method is this?

Accepted Answer

Cluster sampling

Question 12

Which of the following best describes the 'gold standard' in experimental design?

Accepted Answer

Randomization with placebo/treatment groups

Question 13

A teacher wants to select a sample of 6 students from a class of 30. She assigns each student a number and uses a random number generator to select 6 numbers. What type of sample is this?

Accepted Answer

Simple random sample

Question 14

Which of the following is a key difference between cluster sampling and stratified sampling?

Accepted Answer

Cluster sampling selects entire groups, while stratified sampling selects individuals from each group.

Question 15

A researcher wants to ensure that both men and women are equally represented in a sample. She divides the population by gender and randomly selects an equal number from each group. What sampling method is this?

Accepted Answer

Stratified sampling

Question 16

Which of the following is NOT a valid reason for using randomization in experiments?

Accepted Answer

To guarantee that the results are generalizable to the entire population.

Question 17

A researcher selects every 10th patient entering a hospital for a survey. What is the main potential weakness of this sampling method?

Accepted Answer

It may introduce periodicity bias if there is a pattern in patient arrivals.

Question 18

In a study, researchers use existing data to analyze the relationship between air pollution and asthma rates in different cities. What type of study is this?

Accepted Answer

Observational study

Question 19

Which of the following best describes multistage sampling?

Accepted Answer

A sampling method that combines two or more sampling techniques in stages.

Question 20

A study randomly assigns 1,000 participants to receive either a new vaccine or a placebo, and neither the participants nor the researchers know who receives which. After one year, infection rates are compared. What is the main advantage of this design?

Accepted Answer

It minimizes both subject and experimenter bias, allowing for a more accurate assessment of the vaccine's effect.

Chapter 1: Introduction to Statistics – Collecting Sample Data

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