A confidence interval is defined as an estimate of population interval which is calculated from data observed. It provides a range in which the unknown population parameters lies i.e., it offers the upper and lower end values. However, to realize this, it is essential for a person to set his/her desired confidence levels. The commonly used include 90%, 95% and 99%. The width of the confidence interval varies depending on several factors including sample size, sample variability and chosen confidence level.
Generally, an increase in confidence level results in a corresponding increase in confidence interval. In other words, the interval at 99% is higher than that at 95%. To illustrate this, an example with known population standard deviation will be used to calculate confidence interval for the mean at 80%, 95% and 99% confidence levels.
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In this case, I will consider an experiment that found the mean rainfall for 9 cities in January as 98mm, with a population standard deviation of 1.4. following this, the confidence interval will be computed using the formula below
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where x̄ = sample mean (not population mean)
z= equivalent z-score for confidence level (i.e., 80%=1.28 ,95%= 1.96, 99%= 2.58)
σ = population standard deviation
n= sample size
Substituting The Values
80% confidence level
= (97.4, 98.60)
95% confidence
= (97.09, 98.91)
99% confidence level
= (96.8, 99.2)
This implies that the population mean for rainfall in these cities lies between 97.4 to 98.60 at 80% confidence level and the same applies for ranges of both 95% and 99%. However, a common observation is that, an increase in confidence level is associated with an increase in confidence interval. For instance, in this case, the range at 99% is 2.4 while that of 80% is 1.2.
