Interval Estimate:

Interval estimation is the process of calculate the interval for possible value of unknown parameter in the population.

It is calculate in the use of sample data and contrast to the point estimation. It is different from the point estimation. It is the outcome of a statistical
analysis.
The most common forms of interval estimations as follows:

A frequents Method or Confidence interval

A Bayesian method or credible intervals
The other common methods for interval estimations are

Tolerance interval

Prediction interval
And another one is known as the fiducial inference.
Construction of interval estimates parameter:
The normal form of interval estimate of the population parameter is,

Point estimate of parameter and

Plus or minus margin of error
Margin of error:

The amount which is subtracted or added from the point estimate of the statistic and produce the parameter interval estimate is known as the
margin of error.

The margin of error size depends on the following factors:

Sampling distribution type of sample statistics.

Area under sampling distribution percentage that includes the researchers decision.Usually we consider the confident
level as 90%, 95%, 99%.

The interval of each interval estimates are constructed in the region of the point estimate with its confident level.
Construction of Interval estimate for Population mean

Take the point estimate of μ that is the sample mean`vecx`

Define the mean distribution for the sample.When the value of n is large we have to use the central limit theorem. And is
the normal distribution with the,
standard deviation `sigma``vecx`
= `sigma/sqrt(n)`
and mean μ.

Choose the most common confident level as 95%

Find the margin of error which is related with the confidence level.

The area under the curve of the sample means the normal distribution contains the 95% of the interval from.
z= 1.96 to
z= 1.96

The interval estimate for 95 % is,
`vecx` 1.96 (`sigma/sqrt(n)` ) to `vecx``sigma/sqrt(n)`