AP Stats Stats: Evaluation Overview 3 — Questions and Answers
Question 1: When comparing the mean and median of a right-skewed distribution, which statement is typically true?
- Mean < Median
- Mean = Median
- Mean > Median (Correct answer)
- The relationship cannot be determined
Correct answer: Mean > Median
In a right-skewed distribution, the long tail pulls the mean toward higher values, so mean > median.
Question 2: A student calculates r² = 0.81 for a linear regression. What does this mean?
- The slope of the regression line is 0.81
- 81% of the variation in y is explained by the linear relationship with x (Correct answer)
- The correlation is 0.81
- 81% of data points fall on the regression line
Correct answer: 81% of the variation in y is explained by the linear relationship with x
R-squared represents the proportion of variability in the response variable explained by the least-squares regression on the explanatory variable.
Question 3: In a two-sample t-test, what does the null hypothesis typically state?
- μ₁ > μ₂
- μ₁ ≠ μ₂
- μ₁ - μ₂ = 0 (Correct answer)
- The samples are from the same population
Correct answer: μ₁ - μ₂ = 0
The null hypothesis for a two-sample t-test states there is no difference between the two population means (μ₁ - μ₂ = 0).
Question 4: Which of the following sampling methods is most likely to produce a biased sample?
- Simple random sample
- Stratified random sample
- Voluntary response sample (Correct answer)
- Systematic random sample
Correct answer: Voluntary response sample
Voluntary response samples are biased because people with strong opinions are more likely to respond, making the sample unrepresentative.
Question 5: The standard error of a sample mean is calculated as:
- σ / n
- s / √n (Correct answer)
- σ · √n
- s · n
Correct answer: s / √n
The standard error of the sample mean is the sample standard deviation divided by the square root of the sample size.
Question 6: A residual in regression analysis is defined as:
- The predicted value minus the mean of y
- The observed y-value minus the predicted y-value (Correct answer)
- The slope times the x-value
- The difference between two sample means
Correct answer: The observed y-value minus the predicted y-value
A residual is the difference between the observed response and the value predicted by the regression model (y - ŷ).
Question 7: According to the Central Limit Theorem, as sample size increases, the sampling distribution of x̄ approaches:
- The shape of the population distribution
- A uniform distribution
- A normal distribution regardless of population shape (Correct answer)
- A t-distribution with increasing degrees of freedom
Correct answer: A normal distribution regardless of population shape
The Central Limit Theorem states that for large enough sample sizes, the sampling distribution of x̄ is approximately normal regardless of the population's shape.
AP Stats Stats: Evaluation Overview 3
When comparing the mean and median of a right-skewed distribution, which statement is typically true?