Answered: Consider a normal population with mean…

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 normal population with mean = 82 and standard deviation = 12.

If a random sample of size 9 is selected, what is the probability that the sample mean will lie between 80.8 and 83.2 (use RStudio to compute your answer)?

Generate 10 random samples of size 9 from the distribution and calculate the mean for each (create a variable to contain the calculated means). Print out the variable containing your sample means. Based on your answer to part (a), about how many of the sample means would you expect to fall between 80.8 and 83.2? How many of the sample means DID fall between 80.8 and 83.2 (use the sum() function to count this number)?

With a random sample of size 25, what is the probability that the sample mean will fall between 80.8 and 83.2 (use RStudio to compute your answer)?

(d) Generate 10 random samples of size 25 from the distribution and calculate the mean for each (create a variable to contain the calculated means). Print out the variable containing your sample means. For a sample size of 25, about how many of the sample means would you expect to fall between 80.8 and 83.2? How many of the sample means DID fall between 80.8 and 83.2 (use the sum() function to count this number)?

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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