Confidence interval, margin of error, sample size

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 with a specified level of confidence.

Front

What does a 95% confidence interval indicate?

Back

It indicates 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

What is the margin of error?

Back

The margin of error is the amount of error that is allowed in the results of a survey or experiment, often expressed as a percentage.

Front

How is the margin of error calculated?

Back

Margin of error = Z * (σ/√n), where Z is the z-value for the desired confidence level, σ is the population standard deviation, and n is the sample size.

Front

What is the significance of sample size in confidence intervals?

Back

A larger sample size generally leads to a smaller margin of error and a more precise confidence interval.

Front

What does the 'S' represent in the formula for confidence intervals?

Back

The 'S' represents the standard deviation of the sample.

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 do you determine the sample size needed for a specific margin of error?

Back

Sample size can be determined using the formula n = (Z * σ / E)², where E is the desired margin of error.

Front

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

Back

As the confidence level increases, the margin of error also increases, leading to a wider confidence interval.

Front

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

Back

Confidence Interval = sample mean ± (Z * (σ/√n)).