A population consists of the number of siblings for three students. The complete

Question

A population consists of the number of siblings for three students. The complete population is (1, 2, 9). 1) Find the following population parameters: a. The mean ? b. The variance ?2 c. The proportion p of the even numbers 2) Consider selecting, with replacement, a random sample of size n 2 from the population. There are 9 such possible samples, with the first three listed. Complete the table, listing the rest of the possible samples, and the mean, variance, and proportion of even numbers for each sample. Proportion of Even Numbers (p) 0 Sample Mean (R) Variance (s2) 0

Explanation / Answer

Question 2

(1) HEre mean mu = (1 + 2 + 9)/3 = 4

Variance = 1/3 * [(1 - 4)2 + (2 - 4)2 + (9 - 4)2] = 38/3 = 12.6667

Proportion p of even numbers = 1/3 = 0.33

(2) The table is given below

Sample Mean Variance Proportion of even numbers 1 1 1 0 0 1 2 1.5 0.5 0.5 1 9 5 32 0 2 1 1.5 0.5 0.5 2 2 2 0 1 2 9 5.5 24.5 0.5 9 1 5 32 0 9 2 5.5 24.5 0.5 9 9 9 0 0

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