Confidence Interval introduction

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 90% confidence interval mean?

Back

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

Front

How is the margin of error calculated?

Back

The margin of error is calculated as half the width of the confidence interval. It represents the maximum expected difference between the true population parameter and a sample estimate.

Front

What is the interpretation of a confidence interval?

Back

The interpretation of a confidence interval is that we are confident (e.g., 90%, 95%) that the interval contains the true population parameter.

Front

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

Back

The formula is: CI = sample mean ± (critical value) * (standard deviation / √n), where 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 estimate of the population parameter, often due to a small sample size or high variability in the data.

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 population parameter, often due to a large sample size or low variability in the data.

Front

What is the critical value in a confidence interval?

Back

The critical value is a factor used to compute the margin of error, based on the desired confidence level and the distribution of the sample data.

Front

How does sample size affect the confidence interval?

Back

Increasing the sample size generally leads to a narrower confidence interval, which indicates a more precise estimate of the population parameter.

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.