Table of Contents. Peterson, Frank R. Dagostino Book Free Download. Please enter your comment! Please enter your name here. You have entered an incorrect email address! Today Trending. Lee and July 2, Bell Book Free Download May 11, In other words, it is a statistical constant associated with the population.
Examples are population mean, population variance and population standard deviation. A statistic called an unbiased estimator of a population parameter if the mean of the static is equal to the parameter; the corresponding value of the statistic is then called an unbiased estimate of the parameter.
Spiegel, Estimation Theory Statistical inference can be defined as the process by which conclusions are about some measure or attribute of a population eg mean or standard deviation based upon analysis of sample data. Statistical inference can be conveniently divided into two types- estimation and hypothesis testing Lucey, Estimation deals with the estimation of population characteristics such as the population mean and standard deviation from sample characteristic such as the sample mean and standard deviation the population characteristics are known as population parameters whilst to the sample characteristics are known as sample statistics.
An estimate is therefore a statistic obtained from a sample that enables us to make a projection about its corresponding population parameter. Lucey, Types of estimate choice of an estimate : for any given parameter of a population. For example mean x is a point estimate of the population mean u.
We can use mean, medium and mode as an estimate of the population Ugwuga, It is necessary to distinguish between the symbols used for sample statistics and population parameters as follows. Consistency: as the sample size increases, the precision of the estimate of the population parameter also increases.
Efficiency: an estimator is said to be more efficient than another if in repeated sampling, its variance is smaller. Sufficiency: an estimator is said to be sufficient if it uses all the information in the sample estimating the required population parameter Lucey, If we say that a distance is measured as 5.
If on the other hand, we say that the distance is 5. A statement of the error or precision of an estimate is often called its reliability Spiegel and Stephens, This interval has a specified confidence or probability of correcting estimating the true value of the population parameter. Confidence interval estimation of the mean 0 known Confidence What if the sample mean were 21, kilometer? The population mean could be either at the upper limit of the interval or at the lower limits of the interval Ewurum, The distribution that has been developed to be applied to this situation is students t- distribution.
A study of sampling distribution for small sample is called small sampling theory. However a more suitable name would be exact sampling theory, since the result obtained hold for large as well as for small samples Ewurum, Students t -distribution Discovered by W.
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