A estimation the estimation of population parameters

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a. Estimation: The estimation of population parameters such as mean, variance, proportion, etc., from the corresponding sample statistics is an important function of statistics inference. The parameters estimation is very much need for making decision. For example, the manufacturer of electric tubes may be interested in knowing the average life of his product, the scientist may be eager in estimating the average like span of human being and so on. Due to the practical and relative merits of the sample method over the census method, the scientists will prefer the former.

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74 A specific observed value of sample statistic is called estimate. A sample statistics which is used to estimate a population parameter is known as estimator. In other words, sample value is an estimate and the method of estimation (statistical measured) is termed as an estimator. The theory of Estimation was innovate by Prof. R.A. Fisher. Estimation is studied under Point Estimation and Interval Estimation. Good Estimation A good estimator is one which is as close to the true value of population parameter as possible. A good estimator possesses the features which are: a. Un-biasedness: An estimate is said to be unbiased if its expected value is equal to its parameter. For example, if x is an estimate of x will be an unbiased estimate only if, i. E ( x ) = ii. E (S 2 ) = 2 b. Consistency: An estimator is said to be consistent if the estimate tends to approach the parameter as the example size increases. For any distribution, i.e., symmetrical or skewaymmetrc, sample mean, sample variance and sample proportions are consistent estimators of the population mean, population variance and population proportion respectively. c. Efficiency: An estimate is said to be efficient if the variance i.e. (x- ) is minimum. An estimator with less variability is said to be more efficient and consistently more reliable than the other. d. Sufficiency: An estimator which uses all the relevant information in its estimation is said to be sufficient. If the estimator sufficiently insures all the information in the sample, then considering the other estimator is absolutely unnecessary. Point Estimation Method Point Estimation is a single statistic which is used to estimate a population parameter. Now, we shall discuss the sample mean and sample variances are unbiased estimate for corresponding population parameters. Sample Mean and Sample Variance: A sample mean is the best estimator of population mean. It is unbiased, consistent and efficient estimator, and the sampling distribution is closer to normal distribution if so long as sample is sufficiently large. The Central Limit Theorem tells that the sampling distribution mean is equal to the population ( x = ). The variance of sampling distribution is equal to the population variance divided by n n s 2 2 . The standard deviation of the sampling distribution of a statistic is known as its standard error. It is defined as n s x SE
75 Interval Estimation Method

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