AP Stats Confidence Intervals and Estimation 2

Question 1

A 95% confidence interval for a population mean is (42.1, 47.9). Which interpretation is correct?

Accepted Answer

We are 95% confident the population mean falls between 42.1 and 47.9.

Answer

A confidence interval means we are 95% confident (in the procedure) that the interval captures the true population mean.

Question 2

Which condition must be verified before constructing a one-sample t-interval for a mean when n = 15?

Accepted Answer

The population distribution is approximately normal or the data show no strong skew/outliers.

Answer

For small samples (n < 30), the nearly normal condition must be checked via a dotplot or boxplot.

Question 3

A researcher uses a 99% confidence level instead of 95% for the same data. What happens to the interval?

Accepted Answer

It becomes wider.

Answer

Higher confidence requires a larger critical value (z* or t*), which increases the margin of error and widens the interval.

Question 4

The margin of error in a confidence interval for a proportion is 0.04. If the sample size is quadrupled, the new margin of error is approximately:

Accepted Answer

0.02

Answer

Margin of error is proportional to 1/√n, so quadrupling n cuts the margin of error in half.

Question 5

A confidence interval for a proportion is calculated as (0.58, 0.72). What is the sample proportion p̂?

Accepted Answer

0.65

Answer

The sample proportion is the midpoint of the interval: (0.58 + 0.72)/2 = 0.65.

AP Practice Test