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 2, 3, and 10. that samples of size n 2 are randomly selected with replacement from the population of 2, 3, and 10, Listed below are the nine different samples. Complete parts (a) through (c). 2,2 2,3 2,100 3,2 3,3 3,10 10,2 10,3 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.) b. Compare the population variance to the mean of the sample variances. choose the correct answer below. The population variance is equal to the mean of the sample variances O A. O B. The population variance is equal to the square of the mean of the sample variances click to select your answer(s) o search

Explanation / Answer

a)

1) Find the variance of each of the nine samples

2) Formula=s^2=E(x-x)^2/n-1

3) x-bar=Ex/n

=(2+2)/2=2

4) s^2=(2-2)^2+(2-2)^2/1=0

5) Similarly find for all of them. Table would look like the one below:-

AND final table (summing up of above values)

s^2 Prob

0 3

0.5 2

24.5 2

32 2

b)

population mean=2+3+10/3=5

population variance=(2-5)^2+(3-5)^2+(10-5)^2/3

=9+4+25/3=38/3=12.67

mean of sample variance=(0+0.5+32+0.5+0+24.5+32+24.5+0)/9=12.67

Hence, both are equal. Correct answer is A

c)

Correct answer is D

Values Mean s^2 Probability 2,2 2 0 0.11 2,3 2.5 0.5 0.11 2,10 6 32 0.11 3,2 2.5 0.5 0.11 3,3 3 0 0.11 3,10 6.5 24.5 0.11 10,2 6 32 0.11 10,3 6.5 24.5 0.11 10,10 10 0 0.11

AND final table (summing up of above values)

s^2 Prob

0 3

0.5 2

24.5 2

32 2

b)

population mean=2+3+10/3=5

population variance=(2-5)^2+(3-5)^2+(10-5)^2/3

=9+4+25/3=38/3=12.67

mean of sample variance=(0+0.5+32+0.5+0+24.5+32+24.5+0)/9=12.67

Hence, both are equal. Correct answer is A

c)

Correct answer is D

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