Question

Imagine a population of N = 4 individuals, A, B, C and D. Individuals A and B are planning to vote in favor of a controversial referendum, whereas individuals C and D are planning to vote no. In the foreground of the referendum, you are asked to conduct a poll of n=2 individuals. Considering all conceivable simple random samples without replacement, what is the range in the estimates of the percentage of people who support the referendum?

Answer 1

Suppose your sample is \(\large \{C, D\}\)

They gonna say no, so the percentage in favor is \(0\%\)

Answer 2

That is one extreme, can you guess the other extreme ?

Answer 3

A,B Say yes, so percent in favor is 100%... but not sure how to apply this to this question!

Answer 4

N=2 individuals would be AB, AC, AD, BC, BD and CD without replacement

Answer 5

so minimum = 0
maximum = 100

range = ?

Answer 6

100%?

Answer 7

i think so, if by range they mean max-min

Answer 8

Yes, i think they mean that.. Just wasn't sure how they meant it with their wording... but thanks!

Answer 9

looks good then

Answer 10

What if it were for 3 individuals?

Answer 11

you mean the sample contains 3 individuals, n = 3 ?

Answer 12

Yes

Answer 13

just work worst case and best case

Answer 14

worst case : 2 no, 1 yes

best case : 1 no, 2 yes

Answer 15

is it 50% and 50%?

Answer 16

nope, how did u get 50% ?

Answer 17

Oh wait....
sorry

Answer 18

first is 33%

2 = no
1 = yes, so

Answer 19

or am I off...

Answer 20

looks good!

Answer 21

33.33%

Answer 22

and second is 66 %

Answer 23

so it's 33.33% the answer

Answer 24

Looks good!

Answer 25

Thanks a bunch!

Answer 26

let us understand the key terms:
sample size, n
without replacement

Answer 27

Sample size would be the randomized people in the population being considered. You must realize that sometimes a population is too big that it would not be feasible to include them all in the study so instead we select random people that would best represent a whole population, but if it is small, then it is much easier.

If we want to do a statistical analysis, for example, of a population that is for gun control and against. Say, there are 4 total voters representing of equal number between Republicans and Democrats. Republicans like their guns and Democrats like to control the ownership. Since our population, n, is so small that we can include them all in our list.
They can be grouped accordingly, but at the same time, we can also randomize (assign numbers) them.
\(Voters: 1, 2, 3, 4 \)
where
Republican: 1, 3
Democrat: 2, 4
But in our analysis we only want people that are against the gun control. So, we can immediately tell that we now have a smaller group of people {1, 3}, n = 2.

Now here's the other term, WITHOUT REPLACEMENT
what this means is that if I randomly selected my first selection out 1 and 3, I cannot put the number back into the selection. Meaning if I picked 3, then there is only 1 left to be picked next. If it says WITH REPLACEMENT, after I picked 3, then I put 3 back into the group to be selected and there's a chance that I might pick it again the next round of selection or not.

Answer 28

http://studyzone.org/mtestprep/math8/g/probwithless.cfm