# Math Help - Hypothesis Testing with Binomial Distribution

1. ## Hypothesis Testing with Binomial Distribution

You want to win some money at gambling, and you have practised throwing a die so that it comes up 6 (normal die). Your probability of successes in throwing a 6 is p=0.2. You think this is not good enough, so you practise intensely for a week. At the end of that week, you throw the die 20 times and get a 6 five times.

Do hypothesis test at the 1% level to decide if this result provides statistically significant evidence that you have improved your ability to throw a 6. Take a null hypothesis that there is no change in your ability.

****

My alternative hypothesis : That there is a change and p>0.2
and I know I have to use a 1-sided test.

I'm unable to define the test statistics (although my lecturer says its k=5 where k=# of 6 out of 20 trials).

I'm meant to use the Binomial tables to determine the RR, how do i do this.

Answers given is that: we dont reject null hypothesis, and the rejection region is k>=7.

That's it! =) Please do help, I have an exam tomorrow!

2. I get a p-value of .37035173609733 by setting n=20, p=.2 and x=5 in
Binomial Distribution: Probability Calculator

$H_0=.2" alt="H_0=.2" /> vs. $H_a>.2" alt="H_a>.2" />

the p-value is $P(X\ge 5|p=.2)=.37035173609733$