The purpose and intent of the assignment is to help you better understand the sampling distribution of the mean. The class sampling exercise In class we conducted a sampling exercise. The population consisted of 25 elements. The possible values for the elements in the population ranged from 1 to 9 and were distributed as follows: Value Frequency Proportion Percentage 1 1 0.04 4% 2 2 0.08 8% 3 3 0.12 12% 4 4 0.16 16% 5 5 0.2 20% 6 4 0.16 16% 7 3 0.12 12% 8 2 0.08 8% 9 1 0.04 4% As in the class exercise, 10 elements are drawn replacing each element before the next is drawn. This was done 1000 times. The data set is given in a separate spreadsheet and consists of the numbers drawn for these 1000 draws in the order in which these were drawn. Each line can be considered a With all calculations, include the formula that you used. 26. The ‘event’ is that the mean of a sample is equal to a given value. There are many samples that will have the same mean. How many different ‘events’ are possible? 27. What is the mean of the observed distribution of sample means? 28. What is the standard deviation of the observed distribution of sample means? 29. How does the mean of the distribution of sample means compare to the population mean? 30. How does the standard deviation of the distribution of sample means compare to the population standard deviation?

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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Question

The purpose and intent of the assignment is to help you better understand the sampling distribution of

the mean.

The class sampling exercise

In class we conducted a sampling exercise.

The population consisted of 25 elements.

The possible values for the elements in the population ranged from 1 to 9 and were distributed as

follows:

Value Frequency Proportion Percentage

1 1 0.04 4%

2 2 0.08 8%

3 3 0.12 12%

4 4 0.16 16%

5 5 0.2 20%

6 4 0.16 16%

7 3 0.12 12%

8 2 0.08 8%

9 1 0.04 4%

As in the class exercise, 10 elements are drawn replacing each element before the next is drawn.

This was done 1000 times.

The data set is given in a separate spreadsheet and consists of the numbers drawn for these 1000 draws

in the order in which these were drawn. Each line can be considered a

With all calculations, include the formula that you used.

26. The ‘event’ is that the mean of a sample is equal to a given value. There are many samples that
will have the same mean. How many different ‘events’ are possible?
27. What is the mean of the observed distribution of sample means?
28. What is the standard deviation of the observed distribution of sample means?
29. How does the mean of the distribution of sample means compare to the population mean?

30. How does the standard deviation of the distribution of sample means compare to the
population standard deviation?

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Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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