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Definition: the distribution of values taken by a statistic in a large number of simple random samples of the same size taken from the same population is which of the following types of distributions? Marginal distribution Normal distribution Conditional Distribution Sampling Distribution

Definition: the distribution of values taken by a statistic in a large number of simple random samples of the same size taken from the same population is which of the following types of distributions? Marginal distribution Normal distribution Conditional Distribution Sampling Distribution

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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### Understanding Different Types of Distributions **Definition:** The distribution of values taken by a statistic in a large number of simple random samples of the same size taken from the same population is which of the following types of distributions? - **Marginal distribution** - **Normal distribution** - **Conditional Distribution** - **Sampling Distribution** This statement asks which type of distribution is defined by the variability of a statistic (like the mean or proportion) obtained from multiple random samples of the same size from a population. Out of the options provided, the correct answer is **Sampling Distribution**. #### **Explanation of Options:** 1. **Marginal Distribution** - This is the distribution of values of a single variable without considering the influence of other variables. It represents the proportions or counts of different values in one variable in a contingency table. 2. **Normal Distribution** - A type of continuous probability distribution for a real-valued random variable. Most values cluster around a central region, with values tapering off as they go further from the center, forming a bell-shaped curve. 3. **Conditional Distribution** - This is the distribution of a subset of the data that satisfies a certain condition related to another variable. For instance, if you want to know the distribution of heights given that the individual is male, you're looking at a conditional distribution. 4. **Sampling Distribution** - This is the distribution of a statistic (like a sample mean or sample proportion) that is formed when samples of a specific size are repeatedly taken from the same population. The characteristics of the sampling distribution can be used to make inferences about the population from which the samples are taken. Understanding these different types of distributions is crucial for statistical analysis and helps in making accurate inferences from sample data. For illustrations, graphs often visually represent these definitions: - **Marginal Distribution:** Can be shown using bar charts or pie charts. - **Normal Distribution:** Illustrated with a bell curve. - **Conditional Distribution:** Visualized with segmented bar plots or conditional density plots. - **Sampling Distribution:** Often shown with histograms of the sample statistic to demonstrate variability. By understanding these distributions, students and researchers can grasp the fundamentals of statistical inference and data analysis.
Transcribed Image Text:### Understanding Different Types of Distributions **Definition:** The distribution of values taken by a statistic in a large number of simple random samples of the same size taken from the same population is which of the following types of distributions? - **Marginal distribution** - **Normal distribution** - **Conditional Distribution** - **Sampling Distribution** This statement asks which type of distribution is defined by the variability of a statistic (like the mean or proportion) obtained from multiple random samples of the same size from a population. Out of the options provided, the correct answer is **Sampling Distribution**. #### **Explanation of Options:** 1. **Marginal Distribution** - This is the distribution of values of a single variable without considering the influence of other variables. It represents the proportions or counts of different values in one variable in a contingency table. 2. **Normal Distribution** - A type of continuous probability distribution for a real-valued random variable. Most values cluster around a central region, with values tapering off as they go further from the center, forming a bell-shaped curve. 3. **Conditional Distribution** - This is the distribution of a subset of the data that satisfies a certain condition related to another variable. For instance, if you want to know the distribution of heights given that the individual is male, you're looking at a conditional distribution. 4. **Sampling Distribution** - This is the distribution of a statistic (like a sample mean or sample proportion) that is formed when samples of a specific size are repeatedly taken from the same population. The characteristics of the sampling distribution can be used to make inferences about the population from which the samples are taken. Understanding these different types of distributions is crucial for statistical analysis and helps in making accurate inferences from sample data. For illustrations, graphs often visually represent these definitions: - **Marginal Distribution:** Can be shown using bar charts or pie charts. - **Normal Distribution:** Illustrated with a bell curve. - **Conditional Distribution:** Visualized with segmented bar plots or conditional density plots. - **Sampling Distribution:** Often shown with histograms of the sample statistic to demonstrate variability. By understanding these distributions, students and researchers can grasp the fundamentals of statistical inference and data analysis.
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