AP Stats Confidence Intervals and Estimation 3

Question 1

A 90% confidence interval for μ is (18.2, 23.8). A student claims the interval means 90% of individuals in the population score between 18.2 and 23.8. This statement is:

Accepted Answer

Incorrect; the interval estimates the population mean, not individual values.

Answer

Confidence intervals estimate population parameters (like μ), not individual data values.

Question 2

A random sample of 50 students has a mean score of 78 with s = 10. The t* critical value for a 95% CI with 49 df is approximately 2.010. What is the margin of error?

Accepted Answer

2.84

Answer

ME = t* × s/√n = 2.010 × 10/√50 = 2.010 × 1.414 ≈ 2.84.

Question 3

Which scenario requires a t-interval rather than a z-interval for estimating a population mean?

Accepted Answer

The population standard deviation σ is unknown and must be estimated by s.

Answer

A t-interval is used when σ is unknown; the t-distribution accounts for the added uncertainty of estimating σ with s.

Question 4

A polling organization wants to estimate a proportion with a margin of error of at most 0.03 at 95% confidence. Using z* = 1.96 and p̂ = 0.5, the minimum sample size is approximately:

Accepted Answer

1068

Answer

n = (z*/ME)² × p̂(1-p̂) = (1.96/0.03)² × 0.25 ≈ 42.67² × 0.25 ≈ 1068.

Question 5

When constructing a confidence interval, the 10% condition (n ≤ 0.10N) is needed to ensure:

Accepted Answer

The observations are approximately independent.

Answer

The 10% condition ensures that sampling without replacement doesn't violate the independence assumption used in the standard error formula.

AP Practice Test

AP Practice Test

AP Stats Confidence Intervals and Estimation 3