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 nequals2 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?,4???2?,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 ? 3 2 4 nothing ? 6 3 4 nothing ? 6 4 8 nothing ? 10 14 7 nothing ? 13 8 16 nothing ? 24 18 12 nothing ?(Type integers or fractions. Use ascending order of the sample? medians.)

Explanation / Answer

Three randomly selected households are surveyed. The numbers of people in the households are 2?, 4?, and 12. Assume that samples of size nequals2 are randomly selected with replacement from the population of 2?, 4?, and 12. Listed below are the nine different samples.

Nine samples are :

2,2   2?,4???2?,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.

Here sample size is 2 which is even.

Median = 1st observation 2nd observation / 2

The probability distribution of median is,

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