Confidence Intervals and Estimation Flashcards

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

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

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

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

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

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

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

Answer: It becomes wider.

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

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:

Answer: 0.02

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

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

Answer: 0.65

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

Which of the following would NOT reduce the margin of error in a confidence interval?

Answer: Increasing the confidence level from 95% to 99%.

Increasing the confidence level raises the critical value, which increases (not decreases) the margin of error.

For a one-sample z-interval for a proportion, the standard error is calculated using which formula?

Answer: √(p̂(1-p̂)/n)

The standard error for a sample proportion uses the sample proportion p̂ in place of the unknown population proportion p.