Answered: Consider a population having a discrete…

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

Consider a population having a discrete uniform distribution that places a probability of 0.1 on each of the integers 0 through 9. The mean of this distribution is 4.5 and the standard deviation is 2.872.

(a) Calculate the mean and standard error for the distribution of sample means for sample size 30 for this population.

(b) In RStudio, create a variable containing the means of 50 random samples of size 30 from this population (in your answer, include the code you used to create the variable, but do not print out the listing of the 50 sample means). Remember that the rdunif() function requires the purrr library.

(c) Use the hist() function to create a frequency histogram of the sample means, using the following breaks: 3.0, 3.25, 3.5, 3.75, 4.0, 4.25, 4.5, 4.75, 5.0, 5.25, 5.5, 5.75, 6.0.

(d) Calculate the mean and standard deviation of the sample means.

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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