confidence range problem

A big enterprise joint an inform about differents polls about us candidates to president. this polls give us the next dates:

 people surveyed  poll confidence level  voting intention
 candidate red  1000  80%  28%
 candidate blue  2000  50%  26%
 candidate green  1500  90%  24%
 candidate yellow  200  99% 20%

Suppose you can show this polls to someone but not telling the numbers of survey people nor the confidence level. Select two bets you feel be able to make knowing its something really possible (and even considerably high probably)

resolve

we use the next equation in every candidate

1- candidate yellow

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,2 +-2,58*(0,2*0,8/200)^0,5*[(1000000-200)/(999999)]^0,5=

0,2+- 2,58*0,0283*0,9999=

0,2 +- 0,073

the yellow candidate should have a voting in favor in the range between 12,7% and 27,3% percent. Considering there is a big range you should expect almost every posibility about this candidate sonsidering the poll doesn’t give us a big help.

2- candidate green

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,24 +-1,65*(0,24*0,76/1500)^0,5*[(1000000-1500)/(999999)]^0,5=

0,24+- 1,65*0,011*0,9993=

0,24 +- 0,0181=

Then the green candidate should have a voting intention in favor between 22,19% and 25,81%. Most of surveys respect to the other candidate make a big difference respect to rightness.

3- candidate blue

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,26 +-0,67*(0,26*0,74/2000)^0,5*[(1000000-2000)/(999999)]^0,5=

0,26+- 0,67*0,0098*0,999=

0,26 +- 0,0066=

blue candidate voting intention should be between 25,34% and 26,66%

3- candidate red

P +- Z*(PQ/n)^0,5*[(N-n)/(N-1)]^0,5=

0,28 +1,28*(0,28*0,72/1000)^0,5*[(1000000-1000)/(999999)]^0,5=

0,28+- 0,67*0,0142*0,9995=

0,28 +- 0,0095=

red candidate voting intention should be between 27,05% and 28,95%

 

Possible results

– red candidate should never be down of blue candidate, even they both are in the top compiting for first place.

– yellow candidate even considering he is on the last place can really beat red candidate.

– votes for green and yellow candidate can superb  the plus of red and blue candidaten, surprisily considering they are in the top of table.

Standard

bayes probability case

THe enterprise achetypes need a selection from a sample of people to prove a perfume in order to know the uptake of the product. The sampling is compose for 40 children, 70 women, 60 men and 30 elders. The experiment found a rejection in each group its like this:

children->20%

women->10>

men->30%

elder->40%

its required then to find the percentage of people who reject the product. Using bayes theorem we have:

(0.2)(0.2)+(0.1)(0.35)+(0.3)(0.3)+(0.4)(0.15) =

(0.04)+(0.035)+(0.09)+(0.06)=0.225

Conclusions:

– 22,5% of sample reject the product

– the perfume was more rejected between elders and men than women and childrens

– most of people who reject the perfume were men.

 

Suppose besides that we select randomly a someone who reject the product, ¿what’s the ṕrobability that this someone are a children?

(0.04)/[(0.04)+(0.035)+(0.09)+(0.06)] = 0.04/0.225 = 0,17

– so the probability to this someone select are a children is over 17% aprox.

Standard