# Thread: Hypothesis testing with binomial distribution

1. ## Hypothesis testing with binomial distribution

I am really confused about hypothesis testing, and H0 and H1!

Can someone explain it using the following 2 questions:
1. A game of chance is designed so that each person has a 40% chance of winning. Ten people play the game and seven people win. Is this enough evidence at a 10% significance level to suggest that the probability of winning is in fact greater than 40%?

2. A person has a 15% chance of recovering naturally from a certain type of disease. If a new drug is trialled on 15 people and 4 recover, is this enough evidence at a 10% significance level to suggest that the new drug is effective?

Thanks

2. This is binomial distribution. You should start with assuming that 40 % and 15 % (if the drug is not effective, the prob. should still be 15 %) respectively are actually the real probabilities, and from there create 90 % single sided confidence intervals. If the observed cases (the counted numbers, 7 and 15 resp.) are outside of the intervals, you can consider your initial assumption to be false. 1) and 2) are solved separately of course.