This document discusses two types of statistical estimation: point estimation and interval estimation. Point estimation uses a single value like the sample mean or proportion to estimate an unknown population parameter. Interval estimation constructs a range of values called a confidence interval that is likely to contain the true population parameter value with a given level of confidence, such as 95%. Examples are given of using point estimates to estimate average tree height and constructing a 95% confidence interval for a population mean using sample data.

1. STATISTICAL
INTERFERENCE
ESTIMATION

2. INTRODUCTION
• Estimation is a statistical method used to estimate unknown parameters of
a population based on a sample of data.
• i.e, The objective of estimation is to determine the approximate value of
population parameter on the basis of a sample statistic.
• There are two types of estimation:-
• Point estimation and
• Interval estimation.

3. POINT ESTIMATION
• Point estimation involves using a single value, called a point estimator, to
estimate the unknown population parameter. For example, the sample mean
can be used as a point estimator of the population mean, and the sample
proportion can be used as a point estimator of the population proportion.
• The formula for the sample mean is : x
̄ = Σx i / n
• x
̄ is the mean of the n
• xi is individual values.

4. Cont….
• Example:- Let's say you're interested in estimating the average height
(population parameter) of a certain species of trees in a forest. You collect a
sample of 50 trees and record their heights along with other relevant data.
• Your point estimate for the average height based on your sample data is, for
instance, 120 centimeters. This point estimate represents your best guess for
the population parameter.

5. INTERVAL ESTIMATION
• Interval estimation involves constructing a range of values,
called a confidence interval, that is likely to contain the
unknown population parameter with a certain level of
confidence.
• For example, a 95% confidence interval for the population
mean would contain the true population mean in 95% of all
possible samples.
The formula for a confidence interval for the population mean is :
x
̄ ± 1.96σ/ √n
• For example:- if we want to estimate the average height of a
certain population and have a small sample of 20 individuals,
we could calculate a 95% confidence interval using the t-
distribution. This interval would give us a range, such as 160
to 170 cm, suggesting that we are 95% confident the true
average height falls within this interval based on our sample.

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