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 1, 3, and 8. Assume that samples of size n-2 are randomly selected with replacement from the population of 1, 3, and 8. Listed below are the nine different samples. Complete parts (a) through (c). 1,1 1,3 1,8 3,1 3,3 3,8 8,1 8,3 8,8 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 b. Compare the population median to the mean of the sample medians. Choose the correct answer below. O A. The population median is not equal to the mean of the sample medians (it is also not half or double the mean of the sample medians). O B. The population median is equal to half of the mean of the sample medians. O C. The population median is equal to the mean of the sample medians. O D. The population median is equal to double the mean of the sample medians. c nn the samnla meriane tarnet the val A nf tha nnnn latinn me rian? In neneral rin samnle medians make nnnn astimatnre nf nnn atinn meriane? Whv nr whv nnt?

Explanation / Answer

(a) The median of the 9 samples (1,1) (1,3) (1,8) (3,1) (3,3) (3,8) (8,1) (8,3) (8,8) are

1, 2, 4.5, 2, 3, 5.5, 4.5, 5.5, 8 (median = (first number + second number)/2)

The probabilities of these 9 samples id 1/9.

The median 2, 4.5, 5.5 occurs twice, so their probabilitiy is 1/9+1/9 = 2/9

So, the answer to the first question is

Sample medians = 1, 2, 3, 4.5, 5.5, 8

Probability = 1/9, 2/9, 1/9, 2/9, 2/9, 1/9

(b) Population median is the middle number of 1,3, 8 = 3

Mean of the sample medians = (1+2+3+4.5+5.5+8)/6 = 4

So, the answer is A. - The population median is not equal to the mean of the sample medians.

(c) As the population median is not equal to the mean of the sample medians,

So, the answer is B. - The sample medians do not target the population median, so sample medians do not make good estimators of population medians.

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