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 the symbol p̂ represent?

Back

The symbol p̂ (p-hat) represents the sample proportion, which is the ratio of the number of successes to the total number of observations in a sample.

Front

How do you calculate the sample proportion (p̂)?

Back

The sample proportion (p̂) is calculated by dividing the number of successes (x) by the total number of trials (n): p̂ = x/n.

Front

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

Back

The formula for a confidence interval for a proportion is: p̂ ± Z * √(p̂(1-p̂)/n), where Z is the Z-score corresponding to the desired confidence level.

Front

What is the Z-score for a 90% confidence level?

Back

The Z-score for a 90% confidence level is approximately 1.645.

Front

What is the Z-score for a 99% confidence level?

Back

The Z-score for a 99% confidence level is approximately 2.576.

Front

What is the Z-score for a 98% confidence level?

Back

The Z-score for a 98% confidence level is approximately 2.326.

Front

In the context of confidence intervals, what does 'margin of error' refer to?

Back

The margin of error is the amount added to and subtracted from the sample proportion to create the confidence interval, reflecting the uncertainty in the estimate.

Front

What is the relationship between sample size and the width of a confidence interval?

Back

As the sample size increases, the width of the confidence interval decreases, leading to a more precise estimate of the population parameter.

Front

What is the significance of a 95% confidence interval?

Back

A 95% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 95% of those intervals would contain the true population parameter.