[MUSIC] A confidence interval estimator for a population parameter is a rule for individuating an interval in which it is likely to find the parameter of interest. The estimate is called a confidence interval estimate. Therefore, the aim of the confidence interval estimator is to find the range of values, rather than a single number in order to estimate a population mean. This is possible because sometimes happens that similar populations have been sampled very often and the variance of the interested populations can be assumed, known to a very close approximation based on the past experience. Also, when the sample size n gets larger, we estimate the population variance from the sample by applying the same procedure we use when the variance is known. In sampling from a population, all other things being equal, we have more information about the population if we work with a relatively large sample than it would be if working with a smaller sample. However, this factor is not reflected in a point estimates. Increased precision in the information is reflected in confidence interval estimates. In fact, all other things being equal, the larger the sample size, the narrower the interval estimates. And then, the less the uncertainty on the true value of the parameter. Suppose that we have a random sample, and we find two random variables, C and D, with C less than D. Suppose now that the specific sample values of the random variables C and D are c and d. The interval which goes from C to D, may include or may not, the parameter we are interested in. We cannot be sure about it. However, if we take random samples for repeated times from the population, and we find similar intervals, in the long run a certain percentage of these intervals, such as 95%, or 98%, will contain the true value of the unknown parameter. The interval from c to d is indicated to be a 95% confidence interval estimator for the population proportion. If beta is the unknown parameter, suppose that we find the random variables C and D, such that the probability that beta is in between C and D is equal to 1 minus alpha. Where alpha is any number between zero and one. If the specific sample values of C and D are c and d, then the interval from C to D is 100 times 1 minus alpha percent, confidence interval of beta. The quantity 100(1- alpha)% is the confidence level of the interval. If we sample the population for a large number of times, the true value of the parameter beta will be covered by 100 times 1 minus alpha percent of intervals. The confidence interval calculated is indicated as b between c and d, with 100 times 1 minus alpha percent confidence. [MUSIC]