Confidence Interval Review

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 value of an unknown population parameter. It is expressed with a certain level of confidence, such as 90% or 95%.

Front

How do you interpret a 90% confidence interval?

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

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

Back

The formula is: CI = x̄ ± z*(σ/√n), where x̄ is the sample mean, z is the z-score corresponding to the desired confidence level, σ is the population standard deviation, and n is the sample size.

Front

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

Back

The z-score for a 90% confidence level is 1.64.

Front

What is the margin of error in a confidence interval?

Back

The margin of error is the amount added and subtracted from the sample statistic to create the confidence interval. It reflects the uncertainty associated with the sample estimate.

Front

How do you calculate 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-score for the desired confidence level, σ is the standard deviation, and n is the sample size.

Front

What is the standard deviation's role in constructing a confidence interval?

Back

The standard deviation measures the variability of the sample data. It is used to determine the margin of error and thus affects the width of the confidence interval.

Front

What is the difference between a population parameter and a sample statistic?

Back

A population parameter is a value that describes a characteristic of a population (e.g., population mean), while a sample statistic is a value that describes a characteristic of a sample (e.g., sample mean).

Front

How do you construct a confidence interval for the difference between two population proportions?

Back

The formula is: CI = (p1 - p2) ± z*√[p(1-p)(1/n1 + 1/n2)], where p1 and p2 are the sample proportions, p is the pooled proportion, and n1 and n2 are the sample sizes.

Front

What is a simple random sample?

Back

A simple random sample is a subset of individuals chosen from a larger set, where each individual has an equal chance of being selected.