AP Test Review 4a

Front

What is a confidence interval?

Back

A confidence interval is a range of values, derived from a data set, that is likely to contain the value of an unknown population parameter. It is associated with a confidence level, which quantifies the level of confidence that the parameter lies within the interval.

Front

What does a 94% confidence interval indicate?

Back

A 94% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 94% of those intervals would contain the true population mean.

Front

What is the t* value for a 94% confidence interval with n=20?

Back

The t* value for a 94% confidence interval with n=20 is 2.000.

Front

How do you calculate the margin of error for a proportion?

Back

The margin of error for a proportion can be calculated using the formula: ME = z* * sqrt[(p(1-p)/n)], where z* is the z-score corresponding to the desired confidence level, p is the sample proportion, and n is the sample size.

Front

What is the margin of error at 99% confidence for a sample of 2500 with 570 having a balance of $1000 or more?

Back

The margin of error at 99% confidence for this sample is 0.022.

Front

How does increasing the confidence level affect the margin of error?

Back

Increasing the confidence level results in a larger margin of error because a higher confidence level requires a wider interval to ensure that the true parameter is captured.

Front

What is the standard error of a sample proportion?

Back

The standard error of a sample proportion is calculated as SE = sqrt[(p(1-p)/n)], where p is the sample proportion and n is the sample size.

Front

What is the standard error for a sample proportion of 25% from a sample of 200?

Back

The standard error for a sample proportion of 25% from a sample of 200 is approximately 0.0306.

Front

What is a t-interval?

Back

A t-interval is a type of confidence interval used when the sample size is small (typically n < 30) and/or the population standard deviation is unknown. It uses the t-distribution.

Front

When should you use a z-interval instead of a t-interval?

Back

A z-interval should be used when the sample size is large (n ≥ 30) or when the population standard deviation is known.