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, 4, and 12. Assume that samples of size n-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 2,42,12 4,2 4,4 4,12 12,2 12,4 12,12 a. Find the median of each of the nine samples, then summarize the sampling distribution of the medians in the format of a table representing the probability distribution of the distinct median values. Sample Median Probability Type integers or fractions. Use ascending order of the sample medians.)

Explanation / Answer

The median of a sample of size 2 is computed by simply taking the average of those 2 figures. Therefore for the 9 samples given, the medians are computed as:

(2 + 2)/2 = 2

(2 + 4)/2 = 3

(2 + 12) /2 = 7

(4 + 2)/2 = 3

(4 + 4)/2 = 4

(4 + 12)/2 = 8

(12 + 2)/2 = 7

(12 + 4)/2 = 8

(12 + 12)/2 =12

Therefore now the above values could be used to find the probability distribution of the median as:

P(X = 2) = 1/9 because it happens once in 9 samples

P(X=3) = 2/9 because it happens twice in 9 samples

P(X=4) = 1/9

P(X=7) = 2/9

P(X=8) = 2/9

P(X=12) = 1/9

This is the required probability distribution for the sample medians

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