Testing Hypotheses for Binomial Distributions: A Beginner's Guide

[LBJking123]

Hi, I am trying to teach myself how to test hypotheses for any distribution, but am having some trouble.

X=number chosen each year
θ=Mean number chosen in the population

H0: θ=.5
h1: θ>.5

The random sample of n=4 is 0,1,3,3

Test the Hypotheses at α≤0.05 assuming X is a binomial(5,θ/5).

I am completely lost with how to even start this problem. Any help would be awesome.

 

[chiro]

Hey LBJking123.

First try calculating the value of H0 by finding the probabilities corresponding to theta = 0.5

A hint for this is to get the estimator distribution for theta. You are assuming that X is binomial (5,theta/5), so you need to get the mean and use that as an estimator for theta.

After this you have to use a test to get your final statistic and this can range from using the binomial distribution directly to using something like a likelihood ratio statistic.

What techniques have you covered in class?

 

[LBJking123]

Thanks chiro!
We have covered both of those methods (binomial and likelihood ratio statistic), but I think we are supposed to use the binomial to do this one.
This is what I have so far (I am not very confident):

Sample average = 1.75

So,

Reject H0 if P(X≥1.75, given that X is binomial(5,.1)) ≤ 0.05

Then I figure out 1-P(X≤1.75)=0.08146 which is greater than 0.05 so I reject the null.

It just seems like I am totally missing something...

The mean on the binomial(5,theta/5) is just theta. I don't understand how that helps though.