Question

constructed response questions: statistics
algebra 2 unit 8, lessons 1–9
students should show their reasoning and explain their answers in 2–3 sentences or with mathematical work.

question 1: study design
describe the difference between an observational study and an experimental study. give one example of a research question that would be best answered with an observational study and one example that would be best answered with an experimental study.

question 2: statistical questions
which of the following is a statistical question? explain your reasoning.

• a) how many pages does this textbook have?
• b) what is the typical number of hours high school students spend on homework each night?

Explanation:

For Question 1:

An observational study involves researchers observing and measuring variables without interfering with the subjects, while an experimental study involves actively manipulating an independent variable to test its effect on a dependent variable, often with a control group. An observational study is best for questions where manipulation is unethical or impossible, and an experimental study is best for testing causal relationships.

For Question 2:

A statistical question is one that can be answered by collecting data with variability. Option A has a single fixed answer, while Option B involves data that varies across different students.

Answer:

Question 1:

• Difference: Observational studies only observe subjects without manipulating variables; experimental studies manipulate an independent variable to test effects, often using controls.
• Observational study example: "What is the correlation between smoking and lung cancer rates in adults?" (Cannot ethically force people to smoke to test causation)
• Experimental study example: "Does a new medication lower blood pressure more than a placebo?" (Can assign subjects to medication/placebo groups and measure effects)

Question 2:

B) What is the typical number of hours high school students spend on homework each night?