Question

We have been discussing inference in class for a while now. One of the aspects of the discussion is estimation using a confidence interval. Going into as much detail as you like, explain in your own words the purpose of confidence interval estimation. As part of the explanation, indicate what is being estimated, possibly using an example of some kind.

Answer 1

The purpose of Confidence Interval Estimation is to compute a range of values, which we are certain with a specified percentage of probability will capture the the unknown population parameter.

For example, suppose we want to estimate the average height of a student of the college. For this, first we have get the height of each student of the college and calculate the mean. But this is very difficult since the number of students of the college + N is very large.

For reducing this difficulty, Confidence Interval Estimation of mean height of students the following procedure is adopted:

Step 1: We get a sample number n out of the N students using statistical techniques.

Step 2: Select n students from N students using Simple Random Sample (SRS) technique.

Step 3: Calculate Sample mean () and Sample standard deviation (s)

Step 4: Calculate Standard Error as follows:

SE = s/

Step 5: Select proper value of Significance level .

Step 6: From Table, obtain critical value of t corresponding to degrees of freedom and .

Step 7: Calculate Margin of Error = E = t X SE

Step 8:Finally get the Confidence Interval Estimation of mean height of students as follows:

.