FAST Confidence Intervals and Estimation 3

Question 1

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?

Accepted Answer

t-distribution.

Answer

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

Question 2

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

Accepted Answer

Approaches the standard normal distribution.

Answer

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

Question 3

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

Accepted Answer

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

Answer

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

Question 4

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

Accepted Answer

0.50

Answer

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

Question 5

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

Accepted Answer

Increasing the confidence level from 95% to 99%.

Answer

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

(FAST) Future Aptitude Selection Tool Practice Test

(FAST) Future Aptitude Selection Tool Practice Test

FAST Confidence Intervals and Estimation 3