Question

Three randomly selected households are surveyed. The numbers of people in the households are 1​, 2​, and 12. Assume that samples of size n=2 are randomly selected with replacement from the population of 1​, 2​, and 12. Listed below are the nine different samples. Complete parts​ (a) through​ (c). 1​,1   1​,2   1​,12   2​,1   2​,2   2​,12   12​,1   12​,2   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 __(1,2,1.5),__(3.1.5,2),__(4,3,2),__(6.5,13,8),__(7,12.5,14),__(18,12,,24Probability __,__,__,__,__,__ (Type integers or fractions. Use ascending order of the sample​ medians.)

Answer 1

ANSWER:

Given that,

From the given data:

Sample No        Sample        Median    
    1             1,1       1       
    2          1,2       1.5
    3          1,12          6.5
    4             2,1           1.5
    5             2,2           2
    6             2,12          7
    7             12,1          6.5
    8             12,2          7
    9             12,12         12    

The sample distribution of sample median is

Median       Probability
   1            1/9 = 0.1111
   1.5          2/9 = 0.2222
   2            1/9 =0.1111
   6.5          2/9 = 0.222
   7            2/9 = 0.222
   12           1/9 =0.1111