Answered: A variable of a population has a 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

A variable of a population has a mean of μ=200 and a standard deviation of σ=21

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean _____ and standard deviation _____. (FILL IN THE BLANKS)

b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?

A. Normal distribution.
B. No assumption was made.
C. Uniform distribution.

c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?

A. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
B. Yes, the sampling distribution of the sample mean is always normal.
C. No, the sampling distribution of the sample mean is never normal for a sample size of less than 30.

a. The sampling distribution of the sample mean for samples of size 49 is approximately normally distributed with mean
b. For part (a) to be true, what assumption did you make about the distribution of the variable under consideration?
O A. Normal distribution.
OB. No assumption was made.
OC. Uniform distribution.
c. Is the statement in part (a) still true if the sample size is 16 instead of 49? Why or why not?
O A. No. Because the distribution of the variable under consideration is not specified, a sample size of at least 30 is needed for part (a) to be true.
OB. Yes, the sampling distribution of the sample mean is always normal.
and standard deviation
O C. No, the sampling distribution of the sample mean is never normal for sample size less than 30.

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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