Confidence Intervals and Estimation Flashcards

When the population standard deviation is unknown and the sample size is small, which distribution is used to construct a confidence interval for the mean?

Answer: t-distribution.

The t-distribution is used when σ is unknown and n is small, because it accounts for additional uncertainty in estimating variability.

As degrees of freedom in the t-distribution increase, the t-distribution:

Answer: Approaches the standard normal distribution.

With very large degrees of freedom, the t-distribution's tails shrink and it converges to the z-distribution.

A 99% confidence interval is constructed from a sample. Which of the following is a correct interpretation?

Answer: We are 99% confident that the true population mean lies within this interval.

Confidence is expressed in the long-run reliability of the procedure, not in any single probability statement about the parameter.

If a 95% confidence interval for a proportion is (0.40, 0.60), the point estimate of the proportion is:

Answer: 0.50

The point estimate is the midpoint of the confidence interval: (0.40 + 0.60) / 2 = 0.50.

Which of the following would INCREASE the width of a confidence interval?

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

Higher confidence requires a larger critical value, which increases the margin of error and widens the interval.

A sample of 36 scores has a mean of 80 and standard deviation of 12. The standard error of the mean is:

Answer: 2

Standard error = s / √n = 12 / √36 = 12 / 6 = 2.

Which type of estimation provides a range of values likely to contain the true parameter?

Answer: Interval estimation

Interval estimation yields a range (lower bound, upper bound) that likely contains the population parameter.