The object of taking a random sample from a population and forming a statistic such as the
mean from the data is to avail the approximate the mean of the data of that population. It
always has an issue that how the sample statistic estimates the underlying population value.
This confidence interval addresses the solution of the same issue.
In mathematics the question arises What is Confidence Interval; this term describes the
amount of uncertainty that is associated with a sample estimate of a population parameter.
The estimated range is calculated from the given set of the sample data. If the is observed or
samples are taken repeatedly from the same population and a confidence interval is
calculated for each sample separately then a certain percentage of the interval will refer the
Mathematically confidence interval can be defined as
“An interval in which a measurement or a trial decreases corresponding to a given probability.”
Generally the interest of the confidence interval is placed around the mean thus a 50 percent
confidence interval for a symmetric probability density function would be the interval [-c, c]that
shows the following.
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( ½ ) = -c∫c p(x) dx,
The confidence interval that has a particular confidence level is intended to give the reliability
that if the model of statistics is correct then have all the data that has not been obtained from
The confidence level describes the uncertainty that is related with a sample method. Assume
that the same sampling method we use to select different samples and to compute different
interval that are estimated for each sample.
Some interval estimates would include the true population parameter but its not compulsory
that the confidence interval show the exact value of the parameter always rather than it has a
particular probability of being in the confidence interval gives the data that is actually obtained.
If there is a value that 95 percent confidence level then that means we would expecting 95
percent of the interval estimates to include the population parameter.
Basically the interval estimates are made with the help of point estimates. A point estimate is
the single value that is provided as the estimate of the population parameter of interest. Like
have an example for the mean of some quantity.
An interval estimate reflects a range within which the parameter is estimated to lie.
Confidence intervals are usually presented in tables or graphs along with point estimates of
the equal parameter to show the reliability of the estimates.
Like the reliability of the result of the surveys for the different fields can be described by the
use of confidence intervals.
Now the general question is that how it should be drawn. To express the confidence interval
there are three pieces of information is needed
1. Confidence level
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3. Margin of error
If these inputs are given then the range of the confidence interval is expressed by the sample
statistics ± margin of error and the uncertainty that is associated by the confidence interval is
specified by the confidence level. Generally in the problems the margin of error is not given
but it has to calculate.
There are four steps to construct a confidence level
1. Recognize a sample statistic like sample mean, sample proportion etc.
2. Select a confidence level.
3. Then calculate the margin of error.
4. And then specify the confidence interval.
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