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...


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.






Jun 03, 2022
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