Question

Explain the following in your own words (be specific):

1. What is meant by a 95% confidence interval?
2. What is meant by the true mean and how does it relate to the confidence interval?
3. Explain Standard Error or Margin of error and how it helps define the confidence interval?

Answer 1

1) 95% confidence interval is the interval calculated using the sample values, in which the true value of the unknown population parameter (could be mean/variance/etc) lies 95% of the times. The size or width of the confidence interval varies depending upon the size of the sample, variability of data in the sample and the confidence level selected (95% in this case).

2) True mean refers to the actual mean of the underlying population from which the sample under study has been drawn. Confidence interval of the true mean is used in context of the population mean, and is used to define the range in which the true population mean lies with the chosen level of confidence. E.g., a 95% confidence interval for the True population mean refers to the interval in which the true mean lies 95% of the times.

3) Standard Error or Margin of Error of a statistic is an estimate of the standard deviation of the statistic. This is estimated by dividing the standard deviation of the chosen sample by the size of the sample. When the sampling distribution is normally distributed, Standard Error is used along with the sample mean and normal distribution quantiles, to calculate the confidence interval of the population mean.

E.g., if SE is the Standard Error of the sample mean statistic, and is the sample mean, and 1.96 denotes the 0.975 quantile of the normal distribution, 95% confidence interval for the True Population Mean is given by:

( 1.96 * SE )