Confidence Interval for the Mean (large sample)

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 population parameter (e.g., mean) with a specified level of confidence.

Front

What does a 95% confidence interval mean?

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 mean.

Front

How do you calculate the confidence interval for the mean with a large sample?

Back

The confidence interval for the mean is calculated using the formula: CI = x̄ ± Z * (σ/√n), where x̄ is the sample mean, Z is the Z-value corresponding to the desired confidence level, σ is the standard deviation, and n is the sample size.

Front

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

Back

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

Front

What is the Z-value for a 95% confidence level?

Back

The Z-value for a 95% confidence level is approximately 1.96.

Front

What is the standard deviation?

Back

Standard deviation is a measure of the amount of variation or dispersion in a set of values.

Front

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

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 happens to the confidence interval if the confidence level is increased?

Back

If the confidence level is increased, the width of the confidence interval also increases, resulting in a less precise estimate.

Front

What is the maximum error of estimate (margin of error)?

Back

The maximum error of estimate, or margin of error, is the maximum amount by which the sample estimate may differ from the true population parameter.

Front

How do you find the margin of error for a confidence interval?

Back

The margin of error is calculated as: ME = Z * (σ/√n), where Z is the Z-value for the desired confidence level, σ is the standard deviation, and n is the sample size.