Question

(6) A small population {a,b,c,d,e,f,g,h,i} consists of three strata, namely {a,b,c}, {d,e,f} and {g,h,i}. Provide a method that will draw a stratified random sample of size 3.


The following ``answers'' have been proposed.

(a) Take your sample to be a,d,g, i.e., the first element of each stratum.

(b) Take a three sided fair die (such as a standard die with two faces labeled one, another two faces labeled two, and the last two faces labeled three). Roll this die and if face one shows up take your sample to consist of a,b,c. If the face is two then take your sample to be d,e,f. If the face is three then take your sample to be g,h,i.

(c) Take nine identical looking slips and write the letter a on the first slip. Write the letter b on the second slip and so on, write the letter i on the nineth slip. Then take a bowl and put the slips into the bowl and shake the bowl well. Blind fold a friend and ask him/her to pick three slips one after the other. This should give you the required sample.

(d) Take a die and label the first two faces as a, the second two faces as b and the third two faces as c. Roll the dice and the face that comes up gives us one observation of the stratified random sample. Perform similar experiments for the second and the third strata, yielding our required sample.

(e) None of the above.

The correct answer is

Answer 1

The correct answer is option d.

Because in this option the samples are drawn in a probabilistic way. That is all the elements have same probability to be selected. For the 1st strata {a,b,c} if we take a dice which has a on 2 sides b on another 2 sides and c on another 2 sides then if we roll the dice then probability of coming a is 2/6 =1/3 similarly for b and c probability is also = 1/3. So this ia the appropriate way to draw the sample.. repeat similar way for the other 2 strata and we can get the correct stratified random sampling in a right probabilistic way