Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are the nine different samples. Complete parts (a) through (c). 2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9 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 (Type an integer or a fraction. Use ascending order of the sample variances.) b. Compare the population variance to the mean of the sample variances. Choose the correct answer below. O A. The population variance is equal to the square root of the mean of the sample variances. O B. The population variance is equal to the square of the mean of the sample variances. OC. 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?
Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are the nine different samples. Complete parts (a) through (c). 2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9 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 (Type an integer or a fraction. Use ascending order of the sample variances.) b. Compare the population variance to the mean of the sample variances. Choose the correct answer below. O A. The population variance is equal to the square root of the mean of the sample variances. O B. The population variance is equal to the square of the mean of the sample variances. OC. 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 First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:Three randomly selected households are surveyed. The numbers of people in the households are 2, 4, and 9. Assume
that samples of size n = 2 are randomly selected with replacement from the population of 2, 4, and 9. Listed below are
the nine different samples. Complete parts (a) through (c).
2,2 2,4 2,9 4,2 4,4 4,9 9,2 9,4 9,9
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.
Probability
$²
(Type an integer or a fraction. Use ascending order of the sample variances.)
b. Compare the population variance to the mean of the sample variances. Choose the correct answer below.
O 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.
OC. 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?
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