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

Question

Three randomly selected households are surveyed. The numbers of people in the households are 1,2, and 12. Assume that samples of size n 2 are randomly selected with replacement from the population of 1, 2, and 12 through (c). 1,1 1,2 1,12 2.1 2.2 2.12 12.1 12.2 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. 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. OA. The population variance is equal to the mean of the sample variances OB. The population variance is equal to the square of the mean of the sample variances O C. The population variance is equal to the square root of 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, there ore, sa pe variances do not make good esama ars a population variances. O B. The sample vaiances target the population variances, therefore, sample variances make good estimators of population variances C. he sample variances large the opulation vanance therefore, sample vanances do not make aood estimators a population variances. D. The sample variances do not target the population variance, therefore sample variances make good estimators of population anances.

Explanation / Answer

Sample variances can be found using s²=(x-xbar)²/n-1 where xbar is the mean of sample

b.

population variance, sigma²=(x-mu)²/N
Population variance is 24.6667
Average of sample variance is 24.7222

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

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

sample1 sample2 s^2 1 2 0.5 1 2 0.5 1 12 60.5 2 1 0.5 2 2 0 2 12 50 12 1 60.5 12 2 50 12 12 0

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