# JNTU Population Sample and Measures of Central Tendency Questions

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Hoe1111

Jawaharlal Nehru Technological University

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Question 1:

Using your textbook, Peer Reviewed Articles and the Internet, define each of the following terms and provide an example for each, population, sample, measures of central tendency, measures of dispersion, sampling distribution, central limit theorem, confidence interval estimate, and major issues in determining sample size.

Please be sure to include in-text citations and peer reviewed references in APA format in your Answer.

Question 2:

Using your textbook, Peer Reviewed Articles and the Internet, Answer the following,

• 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 a point estimate and an unbiased point estimate? Explain how the sample mean can be an 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 the z statistic for normally distributed populations which eliminates some limitations of the central limit theorem? How is this sampling distribution constructed as a combination of a z distribution and a chi squared distribution? What are the properties of this distribution?

(To provide numerical examples to answer questions mentioned above, for example, in the third item above, you can use the Excel function RAND to generate a sample of a uniform random variable, and the combination of RAND and NORM.INV to generate a sample of a normal random variable).

Please make sure to include in-text citations and peer reviewed references in APA format in your discussion post.

Question 3:

Using your textbook, Peer Reviewed Articles and the Internet, Answer the following,

• What are the major issues in determining the sample size?
• What are five descriptive statistics used to describe the basic properties of variables?
• What is a histogram? What is the advantage of overlaying a normal distribution over a histogram?
• Interpret the frequency distribution from a survey results posted on page 501 of Zikmund et al.textbook (Chapter 20)

Please be sure to include in-text citations and peer reviewed references in APA format in your

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STATISTICS

1

Statistics
Name
Institution
Date

STATISTICS

1.

2

QUESTION 1.

Population sample: A sample is a set of representatives of a population at random. It is a
smaller community that has the features of the whole population taken from the population.
Measures of central tendency: Central patterns can be calculated in three ways, each of which
has a different meaning: mean, median, or mode.
Measures of dispersion: Dispersion is, in other terms, the degree to which the values in a
distribution vary from the distribution average.
Sampling distribution: A distribution of the samples is a theoretical probability distribution of
all available samples of given population size.
Central limit theorem: The theorem implies that the sample's distribution will be approximately
distributed generally if you had a population of average μ and standard deviation β and you took
enough large random samples as a proxy for the population.
Confidence interval estimate: For statistics, an interval of trust coincides with the probability
that a population parameter falls between a collection of values for a certain percentage of
instances. Intervals of confidence in a sample’s method are used to measure uncertainty or
certainty.
Significant issues in determining sample size: Study architecture, sampling method, and
outcome measurements are the variables influencing sample sizes: effect size, standard
deviation, study power, and level of significance. There are variations in the definition and
empirical analysis of the various forms of study architecture.
2. QUESTION 2
A sampled population It is a particular group from which the data is obtained. This could be a
subse...

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