WorksheetsStatistics and ANOVA Quiz
Total questions: 37
Worksheet time: 19mins
Which is NOT a property of the F distribution?
Not symmetric
No negative values
Shape depends on degrees of freedom
Bell-shaped
ANOVA p-value = 0.005. What is the correct conclusion?
At least one variable explains calories
All variables explain calories
None explain calories
Exactly one explains calories
A correlation of −1.5 is possible.
True
False
What is a dummy variable?
Represents categories using two values
Represents numbers using two values
Any variable with two values
Can only be 0 or 1
Which statement is FALSE for one-way ANOVA?
Numerator measures between-group variation
Small F means reject H₀
Rejecting H₀ does not say which mean is different
Small p-value means reject H₀
A golfer studies equipment vs improvement. What is the response variable?
Equipment used
Improvement in performance
What does “correlation does not imply causation” mean?
Correlation does not prove cause-and-effect
Correlation always means causation
Causation never has correlation
Correlation only happens with causation
With positive correlation, as X increases, Y:
Increases
Decreases
ANOVA numerator degrees of freedom equals:
Groups − 1
Total sample size − 1
N − groups
Number of groups
ANOVA is used to test whether:
Population means are equal
Sample sizes differ
Variances are equal
Two variables are related
Rejecting H₀: β₁ = β₂ = 0 means both slopes are non-zero.
True
False, only one may be non-zero
The pooled variance in ANOVA is:
MSE
SSE
√MSE
SSE²
A regression has 4 predictors and n = 44. What are the F-test degrees of freedom?
4 and 39
3 and 40
5 and 38
4 and 40
Smaller F statistic gives stronger evidence against H₀.
True
False
5 groups and 45 students. What are the correct degrees of freedom?
4 and 40
5 and 45
3 and 44
45 and 4
The null hypothesis in one-way ANOVA is:
All population means are equal
All are different
One group is different
No differences exist
MSB measures variation:
Between groups
Within groups
Across samples
Within population
ANOVA denominator degrees of freedom =
N − groups
Groups − 1
N − 1
Groups
The correlation coefficient must be between:
−1 and 1
0 and 1
−1 and 0
Any number
ANOVA alternative hypothesis =
At least one mean is different
All means are equal
No groups differ
Sample sizes differ
All points on regression line → SSE =
0
1
100%
Undefined
In y = β₀ + β₁x , β₁ represents:
Slope
Intercept
Residual
Response value
A residual is negative when:
Observed < predicted
Observed > predicted
Observed = predicted
Always negative
Correlation of 0 means:
No linear relationship
Strong relationship
Error in calculation
Perfect relationship
To compare more than 2 group means, use:
ANOVA
t-test
z-test
Chi-square
p-value = 0.0168 → conclusion:
At least two means differ
All differ
None differ
Exactly two differ
Null hypothesis in multiple regression:
All slopes = 0
At least one slope ≠ 0
Only one slope ≠ 0
All slopes ≠ 1
If all residuals are zero, then:
R² = 1
Slope = 1
Error occurred
r = 0
Adjusted R² accounts for:
Variables and sample size
Correlation strength
Prediction error
Residual size
Two-way ANOVA has how many null hypotheses?
3
1
2
4
Why can’t SST be smaller than SSR?
SST = SSR + SSE
SST is squared
SSE is negative
SSR is fixed
ANOVA hypotheses:
H₀: All means equal, Hₐ: At least one differs
H₀: All differ, Hₐ: All equal
H₀: One differs, Hₐ: All equal
H₀: None equal, Hₐ: All differ
Residual = 0 means:
Predicted = actual
Outlier
r = 1
Prediction error
All points on regression line →
SSR = SST
F = 0
SSE = SST
R² = 0
ANOVA tests are always:
Right-tailed
Left-tailed
Two-tailed
No tail
Relationship between r and slope:
Same sign
Opposite sign
No relation
Random
Difference between r and ρ:
r = sample, ρ = population
r = population, ρ = sample
r = variance, ρ = mean
r = prediction, ρ = slope
