calculating degrees of freedom for 95% confidence

When we need to be really sure about our estimates, such as in life-and-death situations, we choose a 99% confidence level. Typical confidence levels used in practice are 90%, 95%, and 99%. Decreasing the confidence in our estimate makes the confidence interval narrower, and therefore more precise.Ĭonfidence interval estimates are useful when they have the right balance of confidence and precision.Increasing the confidence in our estimate makes the confidence interval wider and therefore less precise.We know that a higher confidence level gives a larger margin of error, so confidence level is also related to precision. In other words, the margin of error is larger. An interval gives a less precise estimate when the interval is wider.In other words, the margin of error is smaller. An interval gives a more precise estimate when the interval is narrower.Let’s quickly review how the precision of a confidence interval relates to the margin of error: The interval width is always twice the margin of error. The interval width is the length of the entire interval on the number line.The margin of error (labeled ME and equal to 1.24 in this example) is the distance that the interval extends to the left and right of the sample mean.The sample mean (9 in this example) is at the center of the interval.

Calculating degrees of freedom for 95% confidence