We cannot say for certain what a and β are without taking an infinite number of measurements. However, we can construct a range of values, called a confidence interval, and say that the parameter is in that range with a certain probability. The formulas on the next page show how to construct such confidence intervals.
Before constructing a confidence interval, you must choose the confidence level. The confidence level is the probability that that population parameter will be in the interval calculated. If you choose a high confidence level, you have a greater chance that the true parameter is in the interval; however, the confidence interval will be larger.
The most common choice for confidence level is the 95% level. That means, there is a 95% chance that the calculated interval contains the true population parameter, and a 5% chance the parameter is outside the interval (2.5% chance too high and 2.5% chance too low). t.05 refers to the t-value for the 95% confidence interval. These t-values must be looked up on a t-test table.