The assets (in billions of dollars) of the four wealthiest people in a particular country are46, 26, 23, 13.Assume that samples of sizen=2are randomly selected with replacement from this population of four values.a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined. xProbability xProbability46nothing 24.5nothing36nothing 23nothing34.5nothing 19.5nothing29.5nothing 18nothing26nothing 13nothing(Type integers or fractions.)b. Compare the mean of the population to the mean of the sampling distribution of the sample mean. The mean of the population,nothing,is▼ greater thanless thanequal tothe mean of the sample means,nothing.(Round to two decimal places as needed.)c. Do the sample means target the value of the population mean? In general, do sample means make good estimates of population means? Why or why not? The sample means▼ do not targettargetthe population mean. In general, sample means▼ do notdomake good estimates of population means because the mean is▼ an unbiaseda biasedestimator.

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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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The assets (in billions of dollars) of the four wealthiest people in a particular country are

46, 26, 23, 13.

Assume that samples of size

n=2

are randomly selected with replacement from this population of four values.

a. After identifying the 16 different possible samples and finding the mean of each sample, construct a table representing the sampling distribution of the sample mean. In the table, values of the sample mean that are the same have been combined.

x	Probability	x	Probability
46	nothing	24.5	nothing
36	nothing	23	nothing
34.5	nothing	19.5	nothing
29.5	nothing	18	nothing
26	nothing	13	nothing

(Type integers or fractions.)

b. Compare the mean of the population to the mean of the sampling distribution of the sample mean.

The mean of the population,

nothing,

▼

greater than

less than

equal to

the mean of the sample means,

nothing.

(Round to two decimal places as needed.)

c. Do the sample means target the value of the population mean? In general, do sample means make good estimates of population means? Why or why not?

The sample means

▼

do not target

target

the population mean. In general, sample means

▼

do not

make good estimates of population means because the mean is

▼

an unbiased

a biased

estimator.

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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