AP Statistics · Topic 9.4
Setting Up a Test for the Slope of a Regression Model Practice
Part of Inference for Quantitative Data: Slopes.(VAR-7.E)
Practice questions
4
Sample questions
4 of 4 — sign in to practice the rest with adaptive difficulty and mastery tracking.
Sample 1difficulty 2/5
A regression of test score on study hours yields slope = 5.2 with SE = 1.3 from n = 25 observations.
At alpha = 0.05, what conclusion for H0: beta = 0?
- A
Cannot test slope this way
- B
Fail to reject H0
- C
Accept H0
- Dcheck_circle
Reject H0; slope is significantly different from 0
Why
With t = 4.0 and df = 23, the p-value is far below 0.05. Reject H0; the slope is statistically significant.
- A
Sample 2difficulty 3/5
H_a: β > 0 is
- Acheck_circle
Right-tailed (one-sided)
- B
Two-sided
- C
Left-tailed
- D
No alternative
Why
Direction "greater than" → right-tail.
- A
Sample 3difficulty 3/5
A researcher hypothesizes positive association: H0: beta = 0 vs Ha: beta > 0. The output reports two-sided p = 0.04 with t = 2.1.
What is the one-sided p-value?
- A
0.96
- B
0.08
- C
0.04
- Dcheck_circle
0.02
Why
For positive Ha with positive t, halve the two-sided p: 0.04/2 = 0.02.
- A
Sample 4difficulty 4/5
Testing H₀: β = 1 (not 0) uses test stat
- A
F = b·SE
- B
t = b/SE(b)
- C
z = b
- Dcheck_circle
t = (b − 1)/SE(b)
Why
General form: t = (b − β₀)/SE(b).
- A