Confidence intervals are used to determine how much latitude there would be in a percent if we were to take repeated samples from the population.
Example
In a study of 150 customers, you find that 60 percent have a college degree. Your best estimate of the percent who have a college degree in the population of customers is also 60 percent. However, since it is just an estimate, we establish confidence intervals around the estimate as a way of showing how reliable the estimate is.
Confidence intervals can be established for any error rate you are willing to accept. If, for example, you choose the 95% confidence interval, you would expect that in five percent of the samples drawn from the population, the percent who had a college degree would fall outside of the interval.
What are the 95% confidence intervals around this percent? In the following example, note that no value is entered for the population size. When the population is very large compared to the sample size (as in most research), it is not necessary to enter a population size. If, however, the sample represents more than ten percent of the population, the formulas incorporate a finite population correction adjustment. Thus, you only need to enter the population size when the sample size exceeds ten percent of the population size.
Enter the percent: 60
Enter the sample size: 150
Enter the population size: (left blank)
Enter the desired confidence interval (%): 95
Standard error of the proportion = .040
Degrees of freedom = 149
95% confidence interval = 60 ± 7.9
Confidence interval range = 52.1 - 67.9
Therefore, our best estimate of the population proportion with 5% error is 60% ± 7.9%. Stated differently, if we predict that the proportion in the population who have a college degree is between 52.1% and 67.9%, our prediction would be wrong for 5% of the samples that we draw from the population.
