Suppose an analyst wants to use the distribution on commodity prices introduced in an article “Commodity-Indexed Debt” in a well-known journal. These prices have a mean of 75 cents and a standard deviation of 9 cents. A sample of 81 commodity prices is selected. Describe the sampling distribution of the mean price for samples of 81 commodity prices. Calculate the mean and standard deviation of the sampling distribution. a. The sampling distribution of the mean price for samples of 81 commodity prices is expected to be normal provided the sample size is small enough with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1. b. The sampling distribution of the mean price for samples of 81 commodity prices is expected to be approximately normal provided the sample size is large enough with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1. c. The sampling distribution of the mean price for samples of 81 commodity prices is expected to be normal provided the sample stays the same with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 9. d. The sampling distribution of the mean price for samples of 81 commodity prices is expected to be approximately normal provided the sample size stays the same with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1. e. The sampling distribution of the mean price for samples of 81 commodity prices cannot be determined for unknown populations.

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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Suppose an analyst wants to use the distribution on commodity prices introduced in an article “Commodity-Indexed Debt” in a well-known journal. These prices have a mean of 75 cents and a standard deviation of 9 cents. A sample of 81 commodity prices is selected. Describe the sampling distribution of the mean price for samples of 81 commodity prices. Calculate the mean and standard deviation of the sampling distribution.

	a.	The sampling distribution of the mean price for samples of 81 commodity prices is expected to be normal provided the sample size is small enough with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1.
	b.	The sampling distribution of the mean price for samples of 81 commodity prices is expected to be approximately normal provided the sample size is large enough with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1.
	c.	The sampling distribution of the mean price for samples of 81 commodity prices is expected to be normal provided the sample stays the same with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 9.
	d.	The sampling distribution of the mean price for samples of 81 commodity prices is expected to be approximately normal provided the sample size stays the same with the average of all sample averages being 75 cents and the standard deviation of all sample averages being 1.
	e.	The sampling distribution of the mean price for samples of 81 commodity prices cannot be determined for unknown populations.

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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