Question 1

Which of the following best describes why random selection is considered fair in statistical studies?

Accepted Answer

Because nobody can predict the outcome before it happens and each outcome is equally likely.

Question 2

A researcher wants to estimate the average height of all university students. She randomly selects 100 students and calculates their mean height. In this context, what is the statistic and what is the parameter?

Accepted Answer

Statistic: the mean height of the sample; Parameter: the mean height of all university students

Question 3

Which of the following sampling methods is most appropriate when the population can be divided into homogeneous groups and you want to ensure representation from each group?

Accepted Answer

Stratified Random Sampling

Question 4

A survey is sent to all students, but only those who feel strongly about the topic respond. What type of bias is most likely present?

Accepted Answer

Voluntary response bias

Question 5

In an experiment, what is the main purpose of randomization?

Accepted Answer

To equalize the effects of unknown or uncontrollable sources of variation across treatment groups

Question 6

Which of the following is NOT a principle of experimental design?

Accepted Answer

Stratify

Question 7

A study assigns one group of patients to receive a new drug and another group to receive a placebo, but neither the patients nor the doctors know who receives which. What is this an example of?

Accepted Answer

Double-blind experiment

Question 8

Which of the following best describes a confounding variable?

Accepted Answer

A variable that is associated with both the explanatory and response variables, making it difficult to determine causality.

Question 9

Suppose you want to study the effect of fertilizer and water on tomato plant growth. You randomly assign plants to receive different combinations of fertilizer and water. What type of experimental design is this?

Accepted Answer

Factorial design

Question 10

Which of the following statements about observational studies is TRUE?

Accepted Answer

They are useful for discovering trends and possible relationships.

Question 11

A researcher wants to compare the effectiveness of two detergents. Detergent A is always used in one washing machine and Detergent B in another. What is the main problem with this experimental setup?

Accepted Answer

There is confounding between detergent and washing machine.

Question 12

Which of the following best describes the placebo effect?

Accepted Answer

A change in the response variable due to the subject's belief in the treatment, not the treatment itself.

Question 13

Which of the following is an example of systematic sampling?

Accepted Answer

Selecting every 10th person from a list after choosing a random starting point.

Question 14

Why is it important to run a pilot study before conducting a full-scale survey?

Accepted Answer

To check for problems in the survey design and identify potential sources of bias.

Question 15

Which of the following best describes the difference between blocking in experiments and stratifying in sampling?

Accepted Answer

Both group similar subjects together and randomize within groups to reduce unwanted variation.

Question 16

A sample statistic is used to estimate a population parameter. Which of the following pairs is correctly matched?

Accepted Answer

$$\bar{y}$$ and $$\mu$$

Question 17

Which of the following is a common mistake that increases bias in sampling?

Accepted Answer

Allowing only those who choose to respond to be counted.

Question 18

In a randomized block design, what is the main purpose of blocking?

Accepted Answer

To isolate variability due to differences between blocks so treatment effects can be seen more clearly.

Question 19

Which of the following is TRUE about pseudorandom numbers generated by computers?

Accepted Answer

They are generated by following a deterministic algorithm and are not truly random.

Question 20

A researcher observes students' study habits and their grades without assigning any treatments. What type of study is this?

Accepted Answer

Observational study

Randomness, Sampling, and Experimental Design in Statistics

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