## Description

Answer to the following questions (APA format not needed):

Please define each of the following terms:sampled population, random sampling, convenient sampling, judgmental sampling, stratified random sampling, consistency in sampling, relative efficiency. Explain why a sample is of probabilistic nature.

What is it meant by the term “parameter of a population”? Explain why a population can be represented by a random variable.

What is a point estimate, and an unbiased point estimate? Explain howthe sample mean can bean unbiased estimate of the population mean.How do you justify that the sample variance is an unbiased estimate of the population variance? What is the sampling requirement in the latter case? Provide a numerical example of estimating the mean, the variance, and the standard deviation.

Please define each of the following terms, discuss applicability and significance of each:sample statistic, standard error, sampling distribution, and central limit theorem. Include hypothetical examples for better clarity.

What is the z statistic and what qualifies a statistic to be z statistic based on the central limit theorem and the basic properties of normal distributions?What are the limitations of the central limit theorem, and how some of these limitations are bypassed?For example, the z statistic as the sampling distribution in estimating a proportion.

What is the sampling distribution in estimating the variance of a population? What are the properties of this distribution?

What is the alternative of z statistic for normally distributed populations whicheliminates some limitations of the central limit theorem?How this sampling distribution is constructed as combination of a z distribution and a chi squared distribution? What are the properties of this distribution?

## Explanation & Answer

Attached.

Running head: PROBABILITY AND DISTRIBUTION

Probability and Distribution

Student’s Name

Institution

Year

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PROBABILITY AND DISTRIBUTION

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1. Please define each of the following terms: sampled population, random sampling,

convenient sampling, judgmental sampling, stratified random sampling, consistency

in sampling, relative efficiency. Explain why a sample is of probabilistic nature.

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Sampled population- It refers to the entire population from which you sample data.

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Random sampling- It is a sampling technique in which each sample unit is based on

chance and every element in the population has an equal probability of being chosen.

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Convenient sampling-It is a non-probability sampling technique in which the sample is

drawn from a part of a population that is convenient to access and which has proximity to

the researcher.

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Judgmental sampling-It is a non-probability sampling technique in which the researcher

selects units to be sampled based on their professional knowledge and judgment.

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Stratified random sampling- It is a probability sampling technique in which the entire

population is divided into groups of elements containing similar characteristics and then

random samples are selected from each of these groups.

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Consistency in sampling- It refers to the attribute of sampled elements showing a uniform

pattern of results as the sample size becomes bigger.

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Relative efficiency-It refers to the ratio of the performance level of one decision-making

unit compared to another.

A population sample is always of probabilistic in nature because it is a portion of the entire

population and thus is used for purposes of making observations and statistical inferences about

the whole population. Therefore, a sample shows the probability of the calculated results being

true in the entire population, thus being probabilistic in nature.

PROBABILITY AND DISTRIBUTION

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2. What is it meant by the term ...