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What Is A Confidence Interval?
Theconfidence intervalrepresents an estimation technique that is used in the field of statistical inference.It allows one or several pairs of values to be defined, among which the specific estimate is investigated.This is within a certain probability.
Astatistical confidence intervalin statistics allows you to calculate the values that exist around a sample mean.Within the sample, there is an upper and a lower range.Within this range, the determined probability is estimated and the population parameter is located.So this allows us to accurately express whether the sample estimate matches the value of the entire population.
What Are The Components Of A Confidence Interval?
Tocalculate a confidence interval, the following elements must be considered:
The size of the sample selection: this depends on the proportion of data used for the calculation of the sample value.It should be observed if it is more or less close to the population parameter.
The level of confidence: this informs in what percentage of cases the estimate is accurate.The levels often range from 95% to 99%.
The margin of error of the estimation: it is indicated as alpha and marks the probability that exists for the population value to be outside the interval.
Estimation of the sample: it is related to the values of the mean, the variance and the differences of the means.The calculation of the interval is based on these values.
What Are Confidence Intervals For?
According to our Confidence Intervals Experts, confidence intervals incompaniesare applied to statistical control of processes.Since the inference process is the one that estimates the value of a parameter from the statistical value, it can be used in a specific way or also by intervals.
Theconfidence intervalrepresents an essential technique in the company.Above all, in the different processes such as the production and sale of goods and services.Having a good statistical control allows knowing the interval that corresponds to each process.With it, the true value of the parameter can be determined, but in cases where this control is not applied, it does not happen in the same way.This makes theconfidence intervalbe used as an excellent parameter for statistical credibility.
Given a random variable with a Normal distribution N (, ), the objective is to construct a confidence interval for the parameter , based on a sample of size n of the variable.
From the didactic point of view, we have to consider two possibilities about the standard deviation of the variable: whether it is known or it is unknown and we have to estimate it from the sample. The case of known , already discussed above, is no more than an academic case with little practical application, however, it is useful from a didactic point of view.
Case of known variance
Given a sample X 1 ... X n, the statistic
is distributed according to a standard Normal. Therefore, applying the pivot method we can construct the expression
With the following program, we can calculate the confidence interval for the mean of a Normal distribution with unknown standard deviation.
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