Binomial distribution and lottery


by FelixHelix
Tags: binomial, distribution, lottery
FelixHelix
FelixHelix is offline
#1
Feb20-12, 04:49 AM
P: 28
Hi there, I'm looking at a problem and wanted some help to advise if I'm going in the right direction.

I need to test if the number of times a lotto ball has appeared in a draw fits a binomial distribution. I have collated the data and ultimately will do a hypothesis test.

The draw consists of 5 balls from 1-50. there have been 347 draws to date and therefore 1735 balls drawn. Taking ball number 1 which has been drawn 31 times as an example I need to check that if the number of times it has been drawn fits a binomial distribution.

I know the formula for the bin. dist but wondered what values for the probability and what number I would need to use. Once I know this would I then set up a hypothesis test at 5% siginificance level to see if the null hypothesis is rejected or accepted?

Thanks for your help in advance.

felix
Phys.Org News Partner Science news on Phys.org
NASA's space station Robonaut finally getting legs
Free the seed: OSSI nurtures growing plants without patent barriers
Going nuts? Turkey looks to pistachios to heat new eco-city
moonman239
moonman239 is offline
#2
Feb20-12, 06:17 PM
P: 300
Quote Quote by FelixHelix View Post
Hi there, I'm looking at a problem and wanted some help to advise if I'm going in the right direction.

I need to test if the number of times a lotto ball has appeared in a draw fits a binomial distribution. I have collated the data and ultimately will do a hypothesis test.

The draw consists of 5 balls from 1-50. there have been 347 draws to date and therefore 1735 balls drawn. Taking ball number 1 which has been drawn 31 times as an example I need to check that if the number of times it has been drawn fits a binomial distribution.

I know the formula for the bin. dist but wondered what values for the probability and what number I would need to use. Once I know this would I then set up a hypothesis test at 5% siginificance level to see if the null hypothesis is rejected or accepted?

Thanks for your help in advance.

felix
What you'd want to do is perform a two-tailed z-test (since np and n(1-p) are > 5) with mean = 347/50 and sd = sqrt(347/50 * 49/50).
FelixHelix
FelixHelix is offline
#3
Feb21-12, 11:41 AM
P: 28
When you say two tailed would my X's (r.v) be the lowest value of a number appearing (in this case 25) and the highest (and 51). Add a continuity correction 24.5 and 51.5 respectively and calculate the z test and see if it is significant?


Register to reply

Related Discussions
Casio fx-9860G - calculating binomial coefficients and binomial distribution General Math 3
Relationship binomial distribution and central limit theorem + poission distribution Set Theory, Logic, Probability, Statistics 1
Binomial probability, similar to lottery problems. Precalculus Mathematics Homework 1
How is the negative binomial the inverse of the binomial distribution? Set Theory, Logic, Probability, Statistics 1
Derivation of the probability distribution function of a binomial distribution General Math 2