TC Flashcard on Confidence Interval

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 used to estimate the uncertainty around a sample statistic.

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.

The sample mean is calculated by adding all the sample values together and dividing by the number of samples.

The formula for a confidence interval for the mean is: CI = sample mean ± (critical value) * (standard deviation / √n), where n is the sample size.

The critical value is a factor used to compute the margin of error in a confidence interval. It is determined by the desired confidence level and the distribution of the data.

As the sample size increases, the confidence interval becomes narrower, indicating a more precise estimate of the population parameter.

Higher confidence levels result in wider confidence intervals, while lower confidence levels result in narrower intervals.

If a confidence interval does not contain the population mean, it suggests that the sample may not be representative of the population, or that the sample size is too small.

A point estimate is a single value estimate of a population parameter, such as the sample mean.

The margin of error is the range of values above and below the sample statistic in a confidence interval, indicating the uncertainty of the estimate.