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Sampling distributions•Parameter•Statistic•Estimator •Point estimator•Commonly used parameters and their estimators•Sampling distribution•Central limit theorem•Use of central limit theorem
Parameter, statistic, estimator, point estimator•Numerical descriptive measures of a population are called parameters•A statistic is a function of the observations in a random sample•An estimator is a statistic that specifies how to use the sample data to estimate an unknown parameter of the population•A point estimator gives a single number as an estimate of the unknown parameter value
Commonly used parameters and estimatorsAll the estimators presented in this table are point estimatorsA realization for an estimator is called an estimateNotation for estimators
Sampling distributionA random variable coming from a population follows a probability distribution and has a standard deviationA function of random variables (estimator) follows a sampling distribution and has a standard deviation called the standard error.EXAMPLE (SAMPLING DISTRIBUTION OF THE MEAN)Let X be the height of a person in the statistics course that provided the dataa)