Answer to Question #311198 in Statistics and Probability for Angel

Question

A group of students got the following scores in an achievement test: 9 12 15 18 21 and 24. Consider sample size of 3 that can be drawn from this population. And construct a sampling distribution of the resulting sample means

Answer 1

Solution

6C3=20

Sample                                 mean

(9,12,15)                               12

(9,12,18)                                 13

(9,12,21)                                 14

(9,12,24)                               15

(9,15,18)                                  14

(9,15,21)                               15           

(9,15,24)                                16

 (9,18,21)                             16

(9,18,24)                               17

(9,21,24)                                 18    

(12,15,18)                            15

(12,15,21)                            16

(12,15,24)                            17

(12,18,21)                            17

(12,18,24)                            18

(12,21,24)                         19

(15,18,21)                               18

(15,18,24)                               19

(15,21,24)                                  20    

(18,21,24)                              21

    

Sampling distribution

E(x)        12    13     14       15         16       17         18         19     20   21 

P[E(x)] 1/20  1/20  1/10   3/20    3/20    3/20   3/20    1/20    1/20   1/20