AP Statistics · Topic 7.4
Setting Up a Test for a Population Mean Practice
Part of Inference for Quantitative Data: Means.(VAR-7.A)
Practice questions
8
Sample questions
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Sample 1difficulty 1/5
A coach claims a new training method reduces 5K times.
Using d = before - after, the appropriate alternative for "training reduces times" is:
- A
Ha: mu_d = 0
- B
Ha: mu_d != 0
- Ccheck_circle
Ha: mu_d > 0
- D
Ha: mu_d < 0
Why
If training reduces times, after < before, so before - after > 0; thus Ha: mu_d > 0.
- A
Sample 2difficulty 2/5
A car maker claims average mileage is at least 35 mpg. Consumer testing yields x-bar = 33.8 with t = -1.40.
Using Ha: mu < 35 with df = 24, the p-value is roughly:
- A
0.50
- Bcheck_circle
0.087
- C
0.913
- D
0.005
Why
For df = 24 and t = -1.40, the lower-tail p-value is about 0.087.
- A
Sample 3difficulty 2/5
A two-sided t-test at alpha = 0.05 with df = 18 has critical values ±2.101.
Which observed t leads to rejection of H0?
- A
t = 1.90
- B
t = 0.00
- Ccheck_circle
t = 2.50
- D
t = -1.50
Why
Reject when |t| > 2.101. Only t = 2.50 satisfies this.
- A
Sample 4difficulty 2/5
A two-sided t-test gives p = 0.06.
A one-sided test in the observed direction would have a p-value of:
- A
0.94
- B
0.06
- C
0.12
- Dcheck_circle
0.03
Why
For a symmetric distribution, the one-sided p in the observed direction is half the two-sided p: 0.06/2 = 0.03.
- A
Sample 5difficulty 3/5
For the same data and direction-matching alternative, one-tailed p-value vs two-tailed
- A
Equal
- Bcheck_circle
One-tailed = (two-tailed)/2
- C
Two-tailed = one-tailed/2
- D
Independent
Why
For symmetric distributions, halving the two-tailed p-value gives one-tailed.
- A