# Test Hypotheses with sample of Binomial RV's

1. May 9, 2013

### 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).

This is what I have so far, but I feel I am completely missing something..

Sample average (Xbar = 1.75

So,

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

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

I know something is not right... Any help would be much appreciated. Thanks!

2. May 10, 2013

### chiro

3. May 10, 2013

### LBJking123

So would I want to do a z score, like on page three of that document? That seems like it would work better.

Then, I get P(Z≥(1.75-.5)/SQRT(.25/4))=P(Z≥5)=0, which is less than 0.05 so I reject the null..?

4. May 10, 2013

### chiro

If that distribution and region corresponds to H0 then yes you reject the null.

Remember that a p-value is looking at a probability for some estimator distribution that relates to a hypothesis.