Interval Estimates

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)`