Answered: . Assuming that 2 of the ages are…

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

The ages (years) of three government officials when they died in office were

54,

45,

and

59.

Complete parts (a) through (d).

a. Assuming that 2 of the ages are randomly selected with replacement, list the different possible samples.

(54,45),(54,59),(45,59)

(54,45),(54,59),(45,54),(45,59),(59,54),(59,45)

(54,54), (54,45),(54,59),(45,45),(45,59),(59,59)

(54,54), (54,45),(54,59),(45,54),(45,45),(45,59),(59,54),(59,45),(59,59)

b. Find the range of each of the samples, then summarize the sampling distribution of the ranges in the format of a table representing the probability distribution.

Sample Range	Probability
	▼ 0 90 45	?
	▼ 54 104 5	?
	▼ 59 113 9	?
	▼ 14 59 118	?

(Type an integer or a fraction.)

c. Compare the population range to the mean of the sample ranges. Choose the correct answer below.

The population range is equal to the mean of the sample ranges.

The population range is not equal to the mean of the sample ranges (it is also not equal to the age of the oldest official or age of the youngest official at the time of death).

The population range is equal to the age of the oldest official at the time of death and the mean of the sample ranges is equal to the youngest official at the time of death.

The population range is equal to the youngest official at the time of death and the mean of the sample ranges is equal to the oldest official at the time of death.

d. Do the sample ranges target the value of the population range? In general, do sample ranges make good estimators of population ranges? Why or why not?

The sample ranges do not target the population range, therefore, sample ranges do not make good estimators of population ranges.

The sample ranges do not target the population range, therefore, sample ranges make good estimators of population ranges.

The sample ranges target the population range, therefore, sample ranges do not make good estimators of population ranges.

The sample ranges target the population range, therefore, sample ranges make good estimators of population ranges.

Click to select your answer(s).

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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