# hypothesis testing for this simple problem

I want to know if my system is functional or not base on 30 trials. so what i did is, I have 1 group with 30 trials. the variable for the group is categorical success or fail. for 30 trials, the system has 30 successes.

how to do the hypothesis testing? i feel like im very wrong.

can i say this? using binomial testing. null hypothesis : the probability of success is 1 which means that the system is functional
alternative hypothesis : the probability of success is not 1 which means that the system is not functional

using 5% significance level i can say that the critical value with n=30 is equal to 30*.05=1.5. calculating the number of trials in which the system fails= 0 fails. with these values 1.5 and 0, 0<1.5. therefore i conclude that the null hypothesis is accepted and the alternative hypothesis is rejected.

• If the null hypothesis is that $p_1$ =$p_2$ and the alternative is $p_1$ not equal to $p_2$ you can't reject the null hypothesis. The way to see is to compute the 95% confidence level for each confidence interval and you will find that they over lap perfectly. This would be true for any confidence level. so you cannot reject the null hypothesis. Commented Jan 21, 2017 at 10:56
• so my hypotheses are wrong and my testing is wrong? what is the proper test for this? Commented Jan 21, 2017 at 12:28
• The exact binomial is fine to use. Commented Jan 21, 2017 at 14:54

Under H0, which assumes that in each run probability of success equals the probability of fails. The probability to obtain N successes is $0.5^N$. In your case p-value= $9.3^{-10}$.