stats for 1st sem MBA atudents hypothesis testing notes
- 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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