AP Statistics · Topic 6.3
Justifying a Claim Based on a Confidence Interval for a Population Proportion Practice
Part of Inference for Categorical Data: Proportions.(UNC-4.B)
Practice questions
7
Sample questions
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Sample 1difficulty 2/5
A poll reports 52% support a candidate, with margin of error ±3 percentage points (95% confidence).
Which is the best interpretation?
- A
Exactly 52% support the candidate.
- Bcheck_circle
We are 95% confident the candidate's true support is between 49% and 55%.
- C
The probability the candidate has 52% support is 0.95.
- D
95% of voters support the candidate within 3 percentage points.
Why
The CI is point estimate ± ME = 52% ± 3% = (49%, 55%).
- A
Sample 2difficulty 2/5
A 95% confidence interval for the proportion of adults who exercise daily is (0.32, 0.40).
Which is the correct interpretation of the interval?
- A
95% of adults exercise daily between 32% and 40% of the time.
- Bcheck_circle
We are 95% confident the true proportion of adults who exercise daily is between 0.32 and 0.40.
- C
95% of samples will have proportions between 0.32 and 0.40.
- D
There is a 95% probability that the true proportion is between 0.32 and 0.40.
Why
Confidence intervals are interpreted as confidence in the procedure capturing the parameter, not probability statements about the fixed parameter.
- A
Sample 3difficulty 3/5
A 95% CI for p is (0.45, 0.55). Test H₀: p = 0.50 vs Hₐ: p ≠ 0.50.
Using α = 0.05, what is the conclusion?
- A
Reject H₀ since 0.50 is in the CI.
- Bcheck_circle
Fail to reject H₀ since 0.50 is in the CI.
- C
Cannot tell without the test statistic.
- D
Reject H₀ since the CI doesn't include 0.
Why
Since 0.50 lies in the 95% CI, the value is plausible; fail to reject H₀ at α = 0.05.
- A
Sample 4difficulty 3/5
A 95% CI for the proportion of left-handed students is (0.08, 0.14).
Which interpretation is INCORRECT?
- A
If we repeated the procedure many times, ~95% of intervals would contain p.
- Bcheck_circle
The probability that p is between 0.08 and 0.14 is 0.95.
- C
We are 95% confident p is between 0.08 and 0.14.
- D
The interval is plausible for p at the 95% level.
Why
The parameter p is fixed; we cannot assign probability to a single fixed-but-unknown value being in a fixed interval.
- A
Sample 5difficulty 3/5
A pollster constructs many 95% confidence intervals for various proportions using independent random samples.
Which statement best interprets "95% confidence"?
- A
95% of the data lies within the interval.
- B
There is a 95% chance the parameter falls in any given interval.
- Ccheck_circle
In repeated sampling, about 95% of such intervals will capture the true proportion.
- D
The procedure produces the correct interval 95% of the time for this single sample.
Why
The confidence level describes the long-run capture rate of the procedure, not a probability for a single interval.
- A