AP Statistics · Topic 7.6
Confidence Intervals for the Difference of Two Means Practice
Part of Inference for Quantitative Data: Means.(UNC-4.G)
Practice questions
8
Sample questions
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Sample 1difficulty 1/5
Two independent samples have n1 = 12, n2 = 20.
Which is the conservative degrees of freedom?
- A
32
- Bcheck_circle
11
- C
30
- D
19
Why
The conservative df is min(n1 - 1, n2 - 1) = min(11, 19) = 11.
- A
Sample 2difficulty 2/5
Two independent random samples of patients are taken from two large hospitals.
The independence condition for the two-sample t requires:
- A
Equal sample sizes.
- B
Equal standard deviations.
- C
Both populations to be normal.
- Dcheck_circle
Independent observations within each sample and between samples.
Why
Standard t requires independence within each sample and between the two samples.
- A
Sample 3difficulty 2/5
Two independent samples: x-bar1 - x-bar2 = 4.5, SE = 1.5, conservative df = 14, t* = 2.145 for 95%.
What is the 95% CI for mu1 - mu2?
- A
(2.00, 7.00)
- B
(3.00, 6.00)
- C
(0.00, 9.00)
- Dcheck_circle
(1.28, 7.72)
Why
ME = 2.145 * 1.5 = 3.22. CI = 4.5 ± 3.22 = (1.28, 7.72).
- A
Sample 4difficulty 2/5
A 95% two-sample t-interval for mu1 - mu2 is (-1.2, 3.4).
What does this imply about a two-sided test of H0: mu1 = mu2 at alpha = 0.05?
- A
Reject H0 because the interval is positive on average.
- B
Reject H0 because the interval is wide.
- Ccheck_circle
Fail to reject H0 because 0 is in the interval.
- D
Cannot determine.
Why
Since 0 lies in the 95% CI, the two-sided test at alpha = 0.05 fails to reject H0.
- A
Sample 5difficulty 2/5
Two-sample t uses the conservative df vs Welch's df.
Compared to Welch's df, the conservative df produces:
- A
a narrower CI
- B
the same CI exactly
- C
a smaller p-value
- Dcheck_circle
a wider CI / larger p-value (more conservative)
Why
Smaller df gives a larger t* and a larger upper-tail probability, hence a wider CI/larger p.
- A