3,3 3,5 3,10 5,3 5 5 5,10 10,3 10,5 10,10. A) Find the variance of each of the n

Question

3,3 3,5 3,10 5,3 5 5 5,10 10,3 10,5 10,10. 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 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 square root of the mean of the sample variances.
C) Do the sample variances target the value of the population variance? Why or why not? a) The sample variances target the population variances, therefore sample variances make good estimators of population variances. b) The sample variances do not target the population variance, therefore sample variances do not make good estimators of population variances. c) The sample variances target the population variance, therefore sample variances do not make good estimators of population variances. d) The sample variances do not target the population variance, therefore sample variances make good estimators of population variances. 3,3 3,5 3,10 5,3 6,5 5,10 10,3 10,5 10,10 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.)

Explanation / Answer

A) The probability table for sample variances will be:

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

C) The sample variances target the population variances, therefore sample variances make good estimators of population variances. Option A is correct.

s^2 Probability 0 1/3 2 2/9 12.5 2/9 24.5 2/9

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