**Understanding Sampling Distributions: A Movie Budget Example**If we took many samples of size 100 from the population of all movies and recorded the mean budget for each sample, what shape do we expect the distribution of sample means to have? Where do we expect it to be centered?**Explanation:**When creating multiple samples of size 100 from a large population (in this case, all movies), and calculating the mean budget for each of these samples, we would expect the distribution of these sample means to form a normal distribution. Despite the shape of the original population distribution, the Central Limit Theory states that the sampling distribution of the sample means will tend to be normal or nearly normal if the sample size is large enough, typically n ≥ 30.The center of this sampling distribution (the mean of the sample means) will be equal to the mean of the population. Thus, the expected value of the sample mean should be the same as the population mean.

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If we took many samples of size 100 from the population of all movies and recorded the mean budget for each sample, what shape do we expect the distribution of sample means to have? Where do we expect it to be centered?

If we took many samples of size 100 from the population of all movies and recorded the mean budget for each sample, what shape do we expect the distribution of sample means to have? Where do we expect it to be centered?

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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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

Question

**Understanding Sampling Distributions: A Movie Budget Example**

If we took many samples of size 100 from the population of all movies and recorded the mean budget for each sample, what shape do we expect the distribution of sample means to have? Where do we expect it to be centered?

**Explanation:**

When creating multiple samples of size 100 from a large population (in this case, all movies), and calculating the mean budget for each of these samples, we would expect the distribution of these sample means to form a normal distribution. Despite the shape of the original population distribution, the Central Limit Theory states that the sampling distribution of the sample means will tend to be normal or nearly normal if the sample size is large enough, typically n ≥ 30.

The center of this sampling distribution (the mean of the sample means) will be equal to the mean of the population. Thus, the expected value of the sample mean should be the same as the population mean.

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