2-Var Quant. Data
What does a positive correlation mean?
As x increases, y increases.
What is a control group? Why is it important?
A group used for comparison; helps establish causality.
State the conditions for constructing a 1-prop z-interval.
Random, 10%, Large Counts (np ≥ 10, n(1−p) ≥ 10)
What is meant by “mutually exclusive” events?
Events that cannot occur together (P(A and B) = 0).
A correlation r = 0.92 is found. Interpret its strength and direction.
Strong positive linear association.
Define replication in an experiment.
Repeating the treatment on many units to reduce variation.
A 95% CI for a population proportion is (0.42, 0.58). Interpret this interval.
We are 95% confident the true proportion is between 0.42 and 0.58.
P(A or B) = P(A) + P(B) − P(A and B). When do you use this?
When events overlap (not mutually exclusive).
What is the slope in a least-squares regression line? What does it mean?
Predicted change in y for each 1-unit increase in x.
What is the difference between an observational study and an experiment?
Only experiments assign treatments and can establish causation.
What does the p-value represent in a 1-prop z-test?
The probability of getting results as extreme or more if H₀ is true.
A bag has 3 red, 2 blue, 5 green marbles. What’s P(red or green)?
(3 + 5)/10 = 0.8
Calculate the residual if observed = 10 and predicted = 8.5
Residual = 10 − 8.5 = 1.5
Explain the purpose of blocking in an experiment.
Grouping similar subjects to reduce variability within treatments.
Calculate the standard error: p̂ = 0.6, n = 100
SE = √(0.6×0.4/100) = 0.049
You toss a coin 5 times. What’s P(all tails)?
(0.5)^5 = 0.03125
If a regression line has R² = 0.64, interpret this.
64% of the variation in y is explained by the model.
Describe a double-blind experiment and its benefits.
Neither subject nor evaluator knows treatment; reduces placebo and bias.
A test gives p = 0.003. What decision should you make at α = 0.05?
Since p < α, reject H₀; evidence supports alternative.
What’s the expected value of a game where you win $10 with P=0.2 and lose $2 with P=0.8?
E(X) = 10×0.2 + (−2)×0.8 = 2 − 1.6 = 0.4