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 value of an unknown population parameter, with a certain level of confidence.

Front

What does the point estimator represent in a confidence interval?

Back

The point estimator is a single value estimate of a population parameter, typically the sample mean, which serves as the center of the confidence interval.

Front

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

Back

The margin of error is calculated by multiplying the critical value (z or t) by the standard error of the sample.

Front

What is the formula for calculating degrees of freedom in a sample?

Back

Degrees of freedom (df) is calculated as n - 1, where n is the sample size.

Front

What effect does increasing the sample size have on the confidence interval?

Back

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

Front

What is the relationship between confidence level and the width of a confidence interval?

Back

As the confidence level increases, the width of the confidence interval also increases, making it less precise.

Front

How do you interpret a 99% confidence interval?

Back

A 99% confidence interval means that if we were to take many samples and build a confidence interval from each sample, approximately 99% of those intervals would contain the true population parameter.

Front

What is the standard error of the mean?

Back

The standard error of the mean is the standard deviation of the sampling distribution of the sample mean, calculated as the population standard deviation divided by the square root of the sample size.

Front

What is the critical value in the context of confidence intervals?

Back

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

Front

What happens to the confidence interval if the confidence level is decreased?

Back

Decreasing the confidence level results in a narrower confidence interval, as it requires less certainty about containing the population parameter.