Confidence Interval (Practice)

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

How do you calculate a confidence interval for a population mean?

Back

To calculate a confidence interval for a population mean, use the formula: 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 does a 95% confidence interval mean?

Back

A 95% confidence interval means that if we were to take 100 different samples and compute a confidence interval for each sample, approximately 95 of the intervals would contain the true population mean.

Front

What is the effect of increasing the sample size on the confidence interval?

Back

Increasing the sample size generally results in a narrower confidence interval, as it reduces the standard error of the mean.

Front

What is the effect of decreasing the confidence level on the confidence interval?

Back

Decreasing the confidence level results in a narrower confidence interval, as it reduces the z-score used in the calculation.

Front

What is the formula for the standard error of the mean?

Back

The standard error of the mean (SEM) is calculated as SEM = σ/√n, where 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 approximately 1.645.

Front

What is the z-score for a 95% confidence level?

Back

The z-score for a 95% confidence level is approximately 1.96.

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

Given a sample mean of 105.2 and a standard deviation of 10, calculate the 90% confidence interval for n=75.

Back

The 90% confidence interval is (103, 107).