Confidence Intervals for Proportions

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 true value of an unknown population parameter, with a specified level of confidence.

Front

What does a 99% confidence interval indicate?

Back

A 99% confidence interval indicates that if we were to take many samples and build a confidence interval from each sample, approximately 99% of those intervals would contain the true population parameter.

Front

What is the symbol for the sample proportion?

Back

p̂ (p-hat)

Front

What factors can affect the width of a confidence interval?

Back

The width of a confidence interval can be affected by the sample size and the confidence level. A larger sample size or a lower confidence level results in a narrower interval.

Front

How do you calculate a confidence interval for a proportion?

Back

A confidence interval for a proportion is calculated using the formula: p̂ ± z*√(p̂(1-p̂)/n), where p̂ is the sample proportion, z* is the critical value, and n is the sample size.

Front

What is the critical value in the context of confidence intervals?

Back

The critical value is a factor used to compute the margin of error in a confidence interval, based on the desired confidence level.

Front

What is the critical value, z*, for a 97% confidence level?

Back

2.17

Front

What happens to the confidence interval if the sample size increases?

Back

If the sample size increases, the confidence interval becomes narrower, assuming the confidence level remains the same.

Front

What does it mean to be 99% confident in a confidence interval?

Back

Being 99% confident means that we believe there is a 99% chance that the true population parameter lies within the calculated confidence interval.

Front

What is the margin of error in a confidence interval?

Back

The margin of error is the range of values above and below the sample statistic in a confidence interval, indicating the uncertainty of the estimate.