Three randomly selected households are surveyed. The numbers of people in the households are 3, 4, and 11. Assume that samples of size n=2 are randomly selected with replacement from the population of 3, 4, and 11. Listed below are the nine different samples. Complete parts (a) through (c). 3,3 3,4 3,11 4,3 4,4 4,11 11,3 11,4 11,11 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. s2 Probability 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. 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. 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 do not target the population variance, therefore, sample variances make good estimators of population variances. C. The sample variances target the population variances, therefore, sample variances make good estimators of population variances. D. The sample variances target the population variance, therefore, sample variances do not make good estimators of population variances.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter10: Statistics

Section10.4: Distributions Of Data

Problem 19PFA

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

and

11.

Assume that samples of size

n=2

are randomly selected with replacement from the population of

and

11.

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

3,3

3,4

3,11

4,3

4,4

4,11

11,3

11,4

11,11

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.

s2	Probability

b. 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.

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.

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

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

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

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