Three randomly selected households are surveyed. The numbers of people in the households are 2 , 4 , and 12 . Assume that samples of size nequals 2 are randomly selected with replacement from the population of 2 , 4 , and 12 . Listed below are the nine different samples. Complete parts (a) through (c). 2 ,2 2 ,4 2 ,12 4 ,2 4 ,4 4 ,12 12 ,2 12 ,4 12 ,12 A) Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values B) Compare the population variance to the mean of the sample variances. Choose the correct answer below. A. The population variance is equal to the square root of the mean of the sample variances. Your answer is not correct. B. The population variance is equal to the square of the mean of the sample variances. C. The population variance is equal to the mean of the sample variances. This is the correct answer. c. Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not? A. The sample variances do not target the population variance, therefore, sample variances do not make good estimators of population variances. B. The sample variances target the population variance, therefore, sample variances do not make good estimators of population variances.

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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Three randomly selected households are surveyed. The numbers of people in the households are

and

Assume that samples of size

nequals

are randomly selected with replacement from the population of

and

Listed below are the nine different samples. Complete parts (a) through (c).

,12

A) Find the variance of each of the nine samples, then summarize the sampling distribution of the variances in the format of a table representing the probability distribution of the distinct variance values

Compare the population variance to the mean of the sample variances. Choose the correct answer below.

The population variance is equal to the square root of the mean of the sample variances.

Your answer is not correct.

The population variance is equal to the square of the mean of the sample variances.

The population variance is equal to the mean of the sample variances.

This is the correct answer.

c. Do the sample variances target the value of the population variance? In general, do sample variances make good estimators of population variances? Why or why not?

The sample variances do not target the population variance, therefore, sample variances do not make good estimators of population variances.

The sample variances target the population variance, therefore, sample variances do not make good estimators of population variances.

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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