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

22,

44,

and

99.

Assume that samples of size

nequals=2

are randomly selected with replacement from the population of

22,

44,

and

99.

Listed below are the nine different samples. Complete parts (a) through (c).

22,22

22,44

22,99

44,22

44,44

44,99

99,22

99,44

99,99

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

nothing

nothing

8

4

6

nothing

11

8.5

5.5

nothing

10

13

6.5

nothing

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Explanation / Answer

(A)

Since there are only 2 data values in the sample so median will be average of these data values. Each of the 9 samples are equally likley so probability of each sample is 1/9 = 0.11111

Following table shows the samples and median:

Following table shows the sampling distribution of sample median:

Samples Median, m P(M=m) 2 2 2 0.11111 2 4 3 0.11111 2 9 5.5 0.11111 4 2 3 0.11111 4 4 4 0.11111 4 9 6.5 0.11111 9 2 5.5 0.11111 9 4 6.5 0.11111 9 9 9 0.11111

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