Mac's Confidence Intervals Review

Front

What is a confidence interval?

Back

A confidence interval is a range of values used to estimate the true value of a population parameter, such as the mean, with a certain level of confidence.

Front

What does a 90% confidence interval mean?

Back

A 90% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 90% of those intervals would contain the true population mean.

Front

How does increasing the sample size affect the confidence interval?

Back

Increasing the sample size generally results in a narrower confidence interval, providing a more precise estimate of the population parameter.

Front

What happens to the confidence interval when the confidence level is increased?

Back

When the confidence level is increased, the confidence interval becomes wider, reflecting greater uncertainty about the estimate.

Front

What is the formula for calculating a confidence interval for a population mean?

Back

The formula is: CI = x̄ ± z*(σ/√n), where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Front

What is the effect of decreasing the confidence level on the confidence interval?

Back

Decreasing the confidence level results in a narrower confidence interval, indicating less certainty about the estimate.

Front

If a confidence interval is (3, 14), does it support the claim that the mean is 2.9?

Back

No, because 2.9 is not within the interval (3, 14).

Front

What is the relationship between sample size and margin of error in a confidence interval?

Back

As the sample size increases, the margin of error decreases, leading to a more precise confidence interval.

Front

What does it mean if a confidence interval does not include zero?

Back

If a confidence interval does not include zero, it suggests that there is a statistically significant difference or effect.

Front

How do you interpret a confidence interval of ($531.92, $841.58)?

Back

This interval suggests that we are 95% confident that the true mean savings account balance of the population lies between $531.92 and $841.58.