Question 1

Which experimental design is best described by the following process: Experimental units are first grouped into homogeneous blocks, and then random assignment to treatments occurs within each block?

Accepted Answer

Block design

Question 2

In a study, 40 students each use two different study techniques in a random order, and their retention scores are compared. What type of experimental design is this?

Accepted Answer

Matched pairs design

Question 3

Why is random assignment of treatments important in an experiment comparing two exercise programs for athletes recovering from hamstring injuries?

Accepted Answer

It helps to evenly distribute uncontrollable and unforeseen factors among treatment groups, reducing bias.

Question 4

A developer randomly assigns 30 driveways to receive fiber-reinforced concrete and 30 to receive standard concrete, then measures crack severity after one year. What is the response variable?

Accepted Answer

Severity of cracks (measured on a scale of 0 to 10)

Question 5

Which of the following best describes a stratified random sample?

Accepted Answer

Divide the population into homogeneous groups (strata), then randomly sample from each group.

Question 6

In the context of experimental design, what is a confounding variable?

Accepted Answer

A variable that is related to both the treatment and the response variable, making it difficult to determine the true effect of the treatment.

Question 7

A city planner wants to survey support for walking trails by randomly selecting 400 residents from different neighborhoods. If she divides the city into neighborhoods and randomly selects residents from each, what sampling method is she using?

Accepted Answer

Stratified random sample

Question 8

In a double-blind experiment, who is unaware of which treatment is being administered?

Accepted Answer

Both the subjects and the researchers measuring the response

Question 9

Suppose a researcher wants to compare three fertilizers on plant growth. She randomly assigns 10 plants to each fertilizer group. What is the experimental design?

Accepted Answer

Completely randomized design

Question 10

Which formula would you use to calculate the mean difference in a matched pairs design?

Accepted Answer

$$\frac{\sum_{i=1}^{n} (X_{i,1} - X_{i,2})}{n}$$

Question 11

A dog food company classifies dogs by breed size before randomly assigning them to two diets. What is the purpose of this classification?

Accepted Answer

To block by breed size and reduce within-treatment variation

Question 12

Which of the following is a potential source of bias when using a cluster sample?

Accepted Answer

Clusters may not be representative of the entire population.

Question 13

In an experiment, what is the main advantage of including a control group?

Accepted Answer

It provides a baseline for comparison to determine the effect of the treatment.

Question 14

Which of the following best describes a response variable?

Accepted Answer

A variable that is measured to assess the effect of treatments

Question 15

A researcher measures the time (in days) for athletes to return to sports after two different exercise programs. The mean for group A is 37.4 days (SD = 27.6), and for group B is 22.2 days (SD = 8.3). Which statistical test would be most appropriate to determine if the difference is significant?

Accepted Answer

A two-sample t-test

Question 16

Which of the following is NOT a valid conclusion from a well-designed experiment with random assignment?

Accepted Answer

Causal inference about the effect of the treatment on all possible populations

Experimental Designs and Data Collection in Introductory Statistics

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