Point Estimator and Confidence Interval

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 In Inferential statistics, we study sample, and use this results to estimate the Population parameters. Suppose we want to know the age of college students, we will random select a sample and calculate the sample mean. This calculated sample mean is the Point estimator.  The Point Estimator is the single value, statistics, computed from a sample, and used to estimate the population parameter.



The Sample mean (point estimator) which is calculated, we are not confident that it represents the mean of the entire population, In inferential statistics, statistician, gives preference to an interval or a range of values, rather than a single digit (Point Estimator). This Range of values or intervals is known as the Confidence Interval.

Confidence Interval is the confidence % age of the range of the values or intervals, which contains the population mean. The confidence level primarily used is 90%, 95%, and 99%. Most commonly used confidence level is 95%. Confidence Interval is calculated using the following formula CI = µ± ME.

ME is the Margin Error, to calculate Confidence interval. We need to calculate the Margin Error first and then we will be able to calculate confidence interval. Margin error can be calculated:-

      1.)  If the Population Variance is known

           2.)  If the Population Variance is not known

If the population variance is known, we use Z – Test, and if it is not known we use T- Test or better known as Student T test.

The formula for Margin error when the Population variance is known as

where 'CI’ is Confidence Interval, X bar refers to the sample mean, Z refers to the critical
value, α refers to the 5%, 1%, and 10%  as per the confidence level we chose for the interval. σ refers to the Population variance, and ‘n’ refers to the number of observations. 

And the formula changes when performing T-test in case when the Population variance is not known, 

Here S stands for Standard Deviation of the Sample, and t refers to the t-test table. There is an assumption made while calculating that the data is normally distributed. This concludes the section of Point Estimators, and Confidence Interval Estimators. The Estimators are supposed to be Unbiased and Efficient for the accurate estimation of the Population parameters.

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