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Simple random sampling, Stratified random sampling, Cluster sampling
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a sample in which each member of the population is equally likely to be included
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Stratified random sampling начать обучение
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a method of sampling that involves the division of a population into smaller sub groups known as strata. In stratified random sampling, or stratification, the strata are formed based on members' shared attributes or characteristics such as income or educational attainment.
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a method where the researcher creates multiple clusters of people from a population where they are indicative of homogeneous characteristics and have an equal chance of being a part of the sample.
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STATISTICAL ESTIMATION начать обучение
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refers to the process by which one makes inferences about a population, based on information obtained from a sample. For example, sample means are used to estimate population means; sample proportions, to estimate population proportions.
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a numer that describes some characteristics of the population
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a numer that describes some characteristics of a sample
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We can think of a statistics as a random variable because it takes numerical value that describe the outcomes of the random sampling proces.
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in order to perform statistical inference начать обучение
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. We need to be able to describe sampling distribution of possible statistics values Different random samples yield different statistics.
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An estimate of a population parameter may be expressed in two ways: начать обучение
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Point estimate or Interval estimate
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A point estimate of a population parameter is a single value of a statistic For example, the sample mean x is a point estimate of the population mean μ. Similarly, the sample proportion p is a point estimate of the population proportion P
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An interval estimate is defined by two numbers, between which a population parameter is said to lie. For example, a x b is an interval estimate of the population mean μ. It indicates that the population mean is greater than a but less than b.
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A good estimator should be PROPERTIES OF GOOD ESTIMATOR начать обучение
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1) unbiased, 2) consistent, 3) relatively efficient
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UNBIASEDNESS of an estimator начать обучение
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An estimator is said to be unbiased if its expected value is identical with the population parameter being estimated. An unbiased estimator is an accurate statistic that's used to approximate a population parameter. Many estimators are “Asymptotically unbiased” in the sense that the biases reduce to practically insignificant value (Zero) when n becomes sufficiently large. “Accurate” in this sense means that it's neither an overestimate nor an underestimate. If an overestimate or underestimate does happen, the mean of the difference is called a “bias.”
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CONSISTENCY of an estimator начать обучение
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If an estimator, say θ, approaches the parameter θ closer and closer as the sample size n increases, θ is said to be a consistent estimator of θ. Stating somewhat more rigorously, the estimator θ is said to be a consistent estimator of θ if, as n approaches infinity, the probability approaches 1 that θ will differ from the parameter θ by no more than an arbitrary constant. The sample mean is an unbiased estimator of µ no matter what form the population distribution assumes, while the sample median is an unbiased estimate of µ only if the population distribution is symmetrical.
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