9. Confidence Intervals Free Online FlashCards

What does a confidence interval estimate?

A confidence interval uses sample data to estimate an unknown population parameter with a range of plausible values, reflecting uncertainty from sampling variability.

What is the general form of a confidence interval?

A confidence interval has the form point estimate ± margin of error, or equivalently, (lower bound, upper bound).

Which sample statistics estimate p and μ?

The point estimate is the sample statistic used to estimate a population parameter: p̂ estimates p, and x̄ estimates μ.

How is the margin of error calculated?

ME = critical value × standard error. The margin of error is the distance from the point estimate to either endpoint.

What does a 95% confidence level mean?

A 95% confidence procedure produces intervals containing the true parameter in about 95% of repeated random samples with the same size and design.

What does a 95% confidence level not mean?

It does not mean there is a 95% probability that one completed interval contains the fixed parameter. The interval changes across samples, but the parameter does not.

What is the one-proportion confidence interval formula?

For a sufficiently large random sample, use p̂ ± z*√[p̂(1−p̂)/n], where p̂ is the sample proportion and n is the sample size.

What conditions support a one-proportion interval?

Check randomness, independence, and large counts: n p̂ ≥ 10 and n(1−p̂) ≥ 10. Without-replacement samples should generally be no more than 10% of the population.

What interval results from x = 232, n = 400, and 95% confidence?

The interval is (0.532, 0.628), or 53.2% to 62.8%. We are 95% confident that this proportion of adults uses the transportation app.

What formula estimates one population mean when σ is unknown?

When σ is unknown, use x̄ ± t* s/√n, where t* comes from a t-distribution with n−1 degrees of freedom.

How are degrees of freedom found for a one-mean t-interval?

For a one-mean t-interval, degrees of freedom equal n − 1.

What conditions support a one-mean t-interval?

Check randomness, independence, and nearly normal data or a sufficiently large sample. Small samples should have no extreme outliers or severe skewness.