Boundary estimation is a statistical method that involves determining the range within which the true value of a population parameter is likely to lie. This range is determined by using sample data to calculate an interval estimate, which is a type of confidence interval.

For example, suppose a researcher wants to estimate the average height of adult men in a certain country. The researcher collects a sample of 100 adult men and measures their heights. The average height of this sample is 175cm, with a standard deviation of 10cm.

To determine the boundary of the estimated average height of adult men in the country, the researcher calculates a confidence interval using the sample data. A 95% confidence interval would be calculated as 175cm +/- 1.96*(10cm/sqrt(100)), resulting in an interval estimate of 160.4cm to 189.6cm. This means that the true average height of adult men in the country is likely to lie within this range with a probability of 95%.

Another example of boundary estimation is in predicting the outcome of an election. Suppose a political pollster wants to estimate the percentage of voters who will support a certain candidate in an upcoming election. The pollster conducts a survey of 1000 voters and finds that 55% of them support the candidate.

To determine the boundary of the estimated percentage of voters who will support the candidate, the pollster calculates a confidence interval using the sample data. A 95% confidence interval would be calculated as 55% +/- 1.96*(sqrt(55%*(100%-55%)/1000)), resulting in an interval estimate of 50.3% to 59.7%. This means that the true percentage of voters who will support the candidate is likely to lie within this range with a probability of 95%.

Boundary estimation is an important tool in statistical analysis as it allows researchers and pollsters to make informed predictions and decisions based on sample data. It helps to provide a level of certainty and confidence in the estimates by providing a range within which the true value is likely to lie. However, it is important to note that the accuracy of the boundary estimation depends on the sample size and the level of confidence chosen. A larger sample size and a higher level of confidence will result in a more precise estimate, but it also means that the range of the estimated boundary will be wider.