7.2 Estimating a Population Proportion

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, indicating the level of uncertainty around that estimate.

Front

What does a 90% confidence level mean?

Back

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

Front

How do you interpret a confidence interval of (0.48, 0.52)?

Back

We are 90% confident that the true proportion of people who approve of the President’s job performance is between 0.48 and 0.52.

Front

What is the critical value for a 98% confidence interval?

Back

The critical value for a 98% confidence interval is 2.326.

Front

What is the z-value for a 95% confidence interval?

Back

The z-value for a 95% confidence interval is 1.96.

Front

How is the margin of error calculated?

Back

The margin of error is calculated by multiplying the critical value by the standard error of the sample proportion.

Front

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

Back

The formula is: CI = 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 does it mean if a confidence interval is wide?

Back

A wide confidence interval indicates a high level of uncertainty about the true population parameter, often due to a small sample size.

Front

What does it mean if a confidence interval is narrow?

Back

A narrow confidence interval indicates a high level of precision in estimating the true population parameter, often due to a large sample size.

Front

What is the relationship between confidence level and margin of error?

Back

As the confidence level increases, the margin of error also increases, resulting in a wider confidence interval.